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SCIENCE 

EVERYDAY 

THINGS 


SCIENC^f 

EVERYDAY 

THINGS 

VOLUME 2: REAL-LIFE PHYSICS 

EDITED BY NEIL SCHLAGER 
WRITTEN BY JUDSDN KNIGHT 

A SCHLAGER INFORMATION GROUP BOOK 


GALE GROUP 



THOMSON LEARNING 

Detroit • New York • San Diego • San Francisco 
Boston • New Haven, Conn. • Waterville, Maine 
London • Munich 




SCIENCE GF EVERYDAY THINGS 

volumez Real-Life physics 

A Schlager Information Group Book 
Neil Schlager, Editor 
Written by Judson Knight 

Gale Group Staff 

Kimberley A. McGrath, Senior Editor 

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Copyright © 2002 

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No part of this book may be reproduced in any form without permission in writing from the publisher, except by a reviewer 
who wishes to quote brief passages or entries in connection with a review written for inclusion in a magazine or newspaper. 

ISBN 0-7876-5631-3 (set) 

0-7876-5632-1 (vol. 1) 0-7876-5634-8 (vol. 3) 

0-7876-5633-X (vol. 2) 0-7876-5635-6 (vol. 4) 

Printed in the United States of America 
10 98765432 1 

Library of Congress Cataloging-in-Publication Data 
Knight, Judson. 

Science of everyday things / written by Judson Knight, Neil Schlager, editor, 
p. cm. 

Includes bibliographical references and indexes. 

Contents: v. 1. Real-life chemistry - v. 2 Real-life physics. 

ISBN 0-7876-5631-3 (set : hardcover) - ISBN 0-7876-5632-1 (v. 1) - ISBN 
0-7876-5633-X (v. 2) 

1. Science-Popular works. I. Schlager, Neil, 1966-11. Title. 



Q162.K678 2001 
500-dc21 


2001050121 





CONTENTS 


I NTRDDUCTIDN V 

Advisory Board vn 


GENERAL CONCEPTS 


Frame of Reference 3 

Kinematics and Dynamics 13 

Density and Volume z 1 

Conservation Laws z 7 


KINEMATICS AND PARTICLE 
DYNAMICS 


Momentum 37 

Centripetal Force -45 

Friction sz 

Laws of Motion 59 

Gravity and Gravitation eg 

Projectile Motion 7 a 

Torque as 

FLUID MECHANICS 

Fluid Mechanics g 5 

Aerodynamics 1 nz 

Bernoulli’s Principle 1 1 z 

Buoyancy 1 z □ 

STATICS 

Statics and Equilibrium 133 

Pressure 140 

Elasticity 14a 


WORK AND ENERGY 


Mechanical Advantage and 


Simple Machines 157 

Energy 1 70 


THERMODYNAMICS 


Gas Laws 133 

Molecular Dynamics 1 gz 

Structure of Matter zo 3 

Thermodynamics z 1 s 

Heat z z 7 

Temperature Z 36 

Thermal Expansion Z45 


WAVE MDTIEIN AND □ S C I L L AT I □ N 


Wave Motion z 5 5 

Oscillation ze 3 

Frequency z 7 1 

Resonance Z 7 a 

Interference zas 

Diffraction zg -4 

Doppler Effect 3 □ 1 


SOUND 

Acoustics 31 1 

Ultrasonics 3 1 g 


LIGHT AND ELECTROMAGNETISM 


Magnetism 331 

Electromagnetic Spectrum 34a 

Light 354 

Luminescence 365 

General Subject Index 373 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2 : REAL-LIFE PHYSICS 



INTRODUCTION 


Overview of the Series 

Welcome to Science of Everyday Things. Our aim 
is to explain how scientific phenomena can be 
understood by observing common, real-world 
events. From luminescence to echolocation to 
buoyancy, the series will illustrate the chief prin- 
ciples that underlay these phenomena and 
explore their application in everyday life. To 
encourage cross-disciplinary study, the entries 
will draw on applications from a wide variety of 
fields and endeavors. 

Science of Everyday Things initially compris- 
es four volumes: 

Volume 1 : Real-Life Chemistry 
Volume 2: Real-Life Physics 
Volume 3: Real-Life Biology 
Volume 4: Real-Life Earth Science 

Future supplements to the series will expand 
coverage of these four areas and explore new 
areas, such as mathematics. 

Arrangement of Real Life 
Physics 

This volume contains 40 entries, each covering a 
different scientific phenomenon or principle. 
The entries are grouped together under common 
categories, with the categories arranged, in gen- 
eral, from the most basic to the most complex. 
Readers searching for a specific topic should con- 
sult the table of contents or the general subject 
index. 

Within each entry, readers will find the fol- 
lowing rubrics: 

• Concept Defines the scientific principle or 
theory around which the entry is focused. 


SCIENCE □ F EVERYDAY THINGS 


• How It Works Explains the principle or the- 
ory in straightforward, step-by-step lan- 
guage. 

• Real-Life Applications Describes how the 
phenomenon can be seen in everyday 
events. 

• Where to Learn More Includes books, arti- 
cles, and Internet sites that contain further 
information about the topic. 

Each entry also includes a “Key Terms” sec- 
tion that defines important concepts discussed in 
the text. Finally, each volume includes numerous 
illustrations, graphs, tables, and photographs. 

In addition, readers will find the compre- 
hensive general subject index valuable in access- 
ing the data. 

Abgut the Editor, Author, 
and Advisory Board 

Neil Schlager and Judson Knight would like to 
thank the members of the advisory board for 
their assistance with this volume. The advisors 
were instrumental in defining the list of topics, 
and reviewed each entry in the volume for scien- 
tific accuracy and reading level. The advisors 
include university-level academics as well as high 
school teachers; their names and affiliations are 
listed elsewhere in the volume. 

neil schlager is the president of 
Schlager Information Group Inc., an editorial 
services company. Among his publications are 
When Technology Fails (Gale, 1994); How 
Products Are Made (Gale, 1994); the St. James 
Press Gay and Lesbian Almanac (St. James Press, 
1998); Best Literature By and About Blacks (Gale, 


VDLUME 2: REAL-LIFE PHYSICS 



Introduction 


2000); Contemporary Novelists, 7th ed. (St. James 
Press, 2000); and Science and Its Times (7 vols., 
Gale, 2000-2001). His publications have won 
numerous awards, including three RUSA awards 
from the American Library Association, two 
Reference Books Bulletin/Booklist Editors’ 
Choice awards, two New York Public Library 
Outstanding Reference awards, and a CHOICE 
award for best academic book. 

Judson Knight is a freelance writer, and 
author of numerous books on subjects ranging 
from science to history to music. His work on 
science titles includes Science, Technology, and 
Society, 2000 b.c.-a.d. 1799 (U*X*L, 2002), 
as well as extensive contributions to Gale’s 
seven-volume Science and Its Times (2000-2001). 
As a writer on history, Knight has published 
Middle Ages Reference Library (2000), Ancient 


Civilizations (1999), and a volume in U*X*L’s 
African American Biography series (1998). 
Knight’s publications in the realm of music 
include Parents Aren’t Supposed to Like It (2001), 
an overview of contemporary performers and 
genres, as well as Abbey Road to Zapple Records: A 
Beatles Encyclopedia (Taylor, 1999). His wife, 
Deidre Knight, is a literary agent and president of 
the Knight Agency. They live in Atlanta with their 
daughter Tyler, born in November 1998. 

Comments and Suggestions 

Your comments on this series and suggestions for 
future editions are welcome. Please write: The 
Editor, Science of Everyday Things, Gale Group, 
27500 Drake Road, Farmington Hills, MI 48331. 


VI 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


ADVISDRY B □ A R D 


William E. Acree, Jr. 

Professor of Chemistry, University of North Texas 

Russell J. Clark 

Research Physicist, Carnegie Mellon University 

Maura C. Flannery 

Professor of Biology, St. John’s University, New 
York 

John Goudie 

Science Instructor, Kalamazoo (MI) Area 
Mathematics and Science Center 

Cheryl Hach 

Science Instructor, Kalamazoo (MI) Area 
Mathematics and Science Center 

Michael Sinclair 

Physics instructor, Kalamazoo (MI) Area 
Mathematics and Science Center 

Rashmi Venkateswaran 

Senior Instructor and Lab Coordinator, 

University of Ottawa 
Ottawa, Ontario, Canada 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


VI 



SCIENCE OF EVERYDAY THINGS 

REAL-LIFE PHYSICS 

GENERAL CONCEPT S 

FRAME □ F REFERENCE 
KINEMATICS AND DYNAMICS 
DENSITY AND VDLUME 
CONSERVATION LAWS 



1 




FRAME 


□ F REFERENCE 


C □ N C E PT 

Among the many specific concepts the student of 
physics must learn, perhaps none is so deceptive- 
ly simple as frame of reference. On the surface, it 
seems obvious that in order to make observa- 
tions, one must do so from a certain point in 
space and time. Yet, when the implications of this 
idea are explored, the fuller complexities begin to 
reveal themselves. Hence the topic occurs at least 
twice in most physics textbooks: early on, when 
the simplest principles are explained — and near 
the end, at the frontiers of the most intellectually 
challenging discoveries in science. 

H □ W IT WDRKS 

There is an old story from India that aptly illus- 
trates how frame of reference affects an under- 
standing of physical properties, and indeed of the 
larger setting in which those properties are man- 
ifested. It is said that six blind men were present- 
ed with an elephant, a creature of which they had 
no previous knowledge, and each explained what 
he thought the elephant was. 

The first felt of the elephant’s side, and told 
the others that the elephant was like a wall. The 
second, however, grabbed the elephant’s trunk, 
and concluded that an elephant was like a snake. 
The third blind man touched the smooth surface 
of its tusk, and was impressed to discover that the 
elephant was a hard, spear-like creature. Fourth 
came a man who touched the elephant’s legs, and 
therefore decided that it was like a tree trunk. 
However, the fifth man, after feeling of its tail, 
disdainfully announced that the elephant was 
nothing but a frayed piece of rope. Last of all, the 
sixth blind man, standing beside the elephant’s 
slowly flapping ear, felt of the ear itself and 

SCIENCE □ F EVERYDAY THINGS 


determined that the elephant was a sort of living 
fan. 

These six blind men went back to their city, 
and each acquired followers after the manner of 
religious teachers. Their devotees would then 
argue with one another, the snake school of 
thought competing with adherents of the fan 
doctrine, the rope philosophy in conflict with the 
tree trunk faction, and so on. The only person 
who did not join in these debates was a seventh 
blind man, much older than the others, who had 
visited the elephant after the other six. 

While the others rushed off with their sepa- 
rate conclusions, the seventh blind man had 
taken the time to pet the elephant, to walk all 
around it, to smell it, to feed it, and to listen to 
the sounds it made. When he returned to the city 
and found the populace in a state of uproar 
between the six factions, the old man laughed to 
himself: he was the only person in the city who 
was not convinced he knew exactly what an ele- 
phant was like. 

Understanding Frame of Ref- 
erence 

The story of the blind men and the elephant, 
within the framework of Indian philosophy and 
spiritual beliefs, illustrates the principle of syad- 
vada. This is a concept in the Jain religion related 
to the Sanskrit word syat, which means “may be.” 
According to the doctrine of syadvada, no judg- 
ment is universal; it is merely a function of the 
circumstances in which the judgment is made. 

On a complex level, syadvada is an illustra- 
tion of relativity, a topic that will be discussed 
later; more immediately, however, both syadvada 
and the story of the blind men beautifully illus- 

VDLUME Z: REAL-LIFE PHYSICS 



Frame of 
Reference 


4 


trate the ways that frame of reference affects per- 
ceptions. These are concerns of fundamental 
importance both in physics and philosophy, dis- 
ciplines that once were closely allied until each 
became more fully defined and developed. Even 
in the modern era, long after the split between 
the two, each in its own way has been concerned 
with the relationship between subject and object. 

These two terms, of course, have numerous 
definitions. Throughout this book, for instance, 
the word “object” is used in a very basic sense, 
meaning simply “a physical object” or “a thing.” 
Here, however, an object may be defined as 
something that is perceived or observed. As soon 
as that definition is made, however, a flaw 
becomes apparent: nothing is just perceived or 
observed in and of itself — there has to be some- 
one or something that actually perceives or 
observes. That something or someone is the sub- 
ject, and the perspective from which the subject 
perceives or observes the object is the subject’s 
frame of reference. 

AMERICA AND CHINA: FRAME 

DF REFERENCE IN PRACTICE. An 

old joke — though not as old as the story of the 
blind men — goes something like this: “I’m glad I 
wasn’t born in China, because I don’t speak Chi- 
nese.” Obviously, the humor revolves around the 
fact that if the speaker were born in China, then 
he or she would have grown up speaking Chi- 
nese, and English would be the foreign language. 

The difference between being born in Amer- 
ica and speaking English on the one hand — even 
if one is of Chinese descent — or of being born in 
China and speaking Chinese on the other, is not 
just a contrast of countries or languages. Rather, 
it is a difference of worlds — a difference, that is, 
in frame of reference. 

Indeed, most people would see a huge dis- 
tinction between an English-speaking American 
and a Chinese-speaking Chinese. Yet to a visitor 
from another planet — someone whose frame of 
reference would be, quite literally, otherworld- 
ly — the American and Chinese would have much 
more in common with each other than either 
would with the visitor. 

The View from Dutside and 
Inside 

Now imagine that the visitor from outer space (a 
handy example of someone with no precon- 
ceived ideas) were to land in the United States. If 

VDLUME z: REAL-LIFE PHYSICS 


the visitor landed in New York City, Chicago, or 
Los Angeles, he or she would conclude that 
America is a very crowded, fast-paced country in 
which a number of ethnic groups live in close 
proximity. But if the visitor first arrived in Iowa 
or Nebraska, he or she might well decide that the 
United States is a sparsely populated land, eco- 
nomically dependent on agriculture and com- 
posed almost entirely of Caucasians. 

A landing in San Francisco would create a 
falsely inflated impression regarding the number 
of Asian Americans or Americans of Pacific 
Island descent, who actually make up only a 
small portion of the national population. The 
same would be true if one first arrived in Arizona 
or New Mexico, where the Native American pop- 
ulation is much higher than for the nation as a 
whole. There are numerous other examples to be 
made in the same vein, all relating to the visitors’ 
impressions of the population, economy, climate, 
physical features, and other aspects of a specific 
place. Without consulting some outside reference 
point — say, an almanac or an atlas — it would be 
impossible to get an accurate picture of the entire 
country. 

The principle is the same as that in the story 
of the blind men, but with an important distinc- 
tion: an elephant is an example of an identifiable 
species, whereas the United States is a unique 
entity, not representative of some larger class of 
thing. (Perhaps the only nation remotely compa- 
rable is Brazil, also a vast land settled by outsiders 
and later populated by a number of groups.) 
Another important distinction between the blind 
men story and the United States example is the 
fact that the blind men were viewing the elephant 
from outside, whereas the visitor to America 
views it from inside. This in turn reflects a differ- 
ence in frame of reference relevant to the work of 
a scientist: often it is possible to view a process, 
event, or phenomenon from outside; but some- 
times one must view it from inside — which is 
more challenging. 

Frame of Reference in Sci- 
ence 

Philosophy (literally, “love of knowledge”) is the 
most fundamental of all disciplines: hence, most 
persons who complete the work for a doctorate 
receive a “doctor of philosophy” (Ph.D.) degree. 
Among the sciences, physics — a direct offspring 
of philosophy, as noted earlier — is the most fun- 

SCIENCE DF EVERYDAY THINGS 


damental, and frame of reference is among its 
most basic concepts. 

Hence, it is necessary to take a seemingly 
backward approach in explaining how frame of 
reference works, examining first the broad appli- 
cations of the principle and then drawing upon 
its specific relation to physics. It makes little 
sense to discuss first the ways that physicists 
apply frame of reference, and only then to 
explain the concept in terms of everyday life. It is 
more meaningful to relate frame of reference first 
to familiar, or at least easily comprehensible, 
experiences — as has been done. 

At this point, however, it is appropriate to 
discuss how the concept is applied to the sci- 
ences. People use frame of reference every day — 
indeed, virtually every moment — of their lives, 
without thinking about it. Rare indeed is the per- 
son who “walks a mile in another person’s 
shoes” — that is, someone who tries to see events 
from the viewpoint of another. Physicists, on the 
other hand, have to be acutely aware of their 
frame of reference. Moreover, they must “rise 
above” their frame of reference in the sense that 
they have to take it into account in making cal- 
culations. For physicists in particular, and scien- 
tists in general, frame of reference has abundant 
“real-life applications.” 

REAL-LIFE 
A P P L I C AT I □ N S 

Points and Graphs 

There is no such thing as an absolute frame of 
reference — that is, a frame of reference that is 
fixed, and not dependent on anything else. If the 
entire universe consisted of just two points, it 
would be impossible (and indeed irrelevant) to 
say which was to the right of the other. There 
would be no right and left: in order to have such 
a distinction, it is necessary to have a third point 
from which to evaluate the other two points. 

As long as there are just two points, there is 
only one dimension. The addition of a third 
point — as long as it does not lie along a straight 
line drawn through the first two points — creates 
two dimensions, length and width. From the 
frame of reference of any one point, then, it is 
possible to say which of the other two points is to 
the right. 

SCIENCE □ E EVERYDAY THINGS 



Lines of longitude on Earth are measured 

AGAINST THE LINE PICTURED HERE! THE “PRIME MERID- 
IAN” RUNNING THROUGH GREENWICH, ENGLAND. An 
IMAGINARY LINE DRAWN THROUGH THAT SPOT MARKS 
THE Y-AXIS FOR ALL VERTICAL COORDINATES ON EARTH , 
WITH A VALUE OF G° ALONG THE X-AXIS, WHICH IS THE 

Equator. The Prime Meridian, however, is an 

ARBITRARY STANDARD THAT DEPENDS ON ONE’S FRAME 

of reference. (Photograph by Dennis di Cicco/Corbis. Repro- 
duced by permission.) 

Clearly, the judgment of right or left is rela- 
tive, since it changes from point to point. A more 
absolute judgment (but still not a completely 
absolute one) would only be possible from the 
frame of reference of a fourth point. But to con- 
stitute a new dimension, that fourth point could 
not lie on the same plane as the other three 
points — more specifically, it should not be possi- 
ble to create a single plane that encompasses all 
four points. 

Assuming that condition is met, however, it 
then becomes easier to judge right and left. Yet 
right and left are never fully absolute, a fact easi- 
ly illustrated by substituting people for points. 
One may look at two objects and judge which is 
to the right of the other, but if one stands on 
one’s head, then of course right and left become 
reversed. 

Of course, when someone is upside-down, 
the correct orientation of left and right is still 

VDLUME 2: REAL-LIFE PHYSICS 


FRAME DF 

Reference 




Frame of 
Reference 


e 


fairly obvious. In certain situations observed by 
physicists and other scientists, however, orienta- 
tion is not so simple. It then becomes necessary 
to assign values to various points, and for this, 
scientists use tools such as the Cartesian coordi- 
nate system. 

COORDINATES AND AXES. 

Though it is named after the French mathemati- 
cian and philosopher Rene Descartes (1596- 
1650), who first described its principles, the 
Cartesian system owes at least as much to Pierre 
de Fermat (1601-1665). Fermat, a brilliant 
French amateur mathematician — amateur in the 
sense that he was not trained in mathematics, nor 
did he earn a living from that discipline — greatly 
developed the Cartesian system. 

A coordinate is a number or set of numbers 
used to specify the location of a point on a line, 
on a surface such as a plane, or in space. In the 
Cartesian system, the x-axis is the horizontal line 
of reference, and the y-axis the vertical line of 
reference. Hence, the coordinate (0, 0) designates 
the point where the x- and y-axes meet. All num- 
bers to the right of 0 on the x-axis, and above 0 
on the y-axis, have a positive value, while those to 
the left of 0 on the x-axis, or below 0 on the y-axis 
have a negative value. 

This version of the Cartesian system only 
accounts for two dimensions, however; therefore, 
a z-axis, which constitutes a line of reference for 
the third dimension, is necessary in three-dimen- 
sional graphs. The z-axis, too, meets the x- and y- 
axes at (0,0), only now that point is designated as 
( 0 , 0 , 0 ). 

In the two-dimensional Cartesian system, 
the x-axis equates to “width” and the y-axis to 
“height.” The introduction of a z-axis adds the 
dimension of “depth” — though in fact, length, 
width, and height are all relative to the observer’s 
frame of reference. (Most representations of the 
three-axis system set the x- and y-axes along a 
horizontal plane, with the z-axis perpendicular 
to them.) Basic studies in physics, however, typi- 
cally involve only the x- and y-axes, essential to 
plotting graphs, which, in turn, are integral to 
illustrating the behavior of physical processes. 

the triple pdint. For instance, 
there is a phenomenon known as the “triple 
point,” which is difficult to comprehend unless 
one sees it on a graph. For a chemical compound 
such as water or carbon dioxide, there is a point 
at which it is simultaneously a liquid, a solid, and 

VDLUME z: real-life physics 


a vapor. This, of course, seems to go against com- 
mon sense, yet a graph makes it clear how this is 
possible. 

Using the x-axis to measure temperature 
and the y-axis pressure, a number of surprises 
become apparent. For instance, most people 
associate water as a vapor (that is, steam) with 
very high temperatures. Yet water can also be a 
vapor — for example, the mist on a winter morn- 
ing — at relatively low temperatures and pres- 
sures, as the graph shows. 

The graph also shows that the higher the 
temperature of water vapor, the higher the pres- 
sure will be. This is represented by a line that 
curves upward to the right. Note that it is not a 
straight line along a 45° angle: up to about 68°F 
(20°C), temperature increases at a somewhat 
greater rate than pressure does, but as tempera- 
ture gets higher, pressure increases dramatically. 

As everyone knows, at relatively low temper- 
atures water is a solid — ice. Pressure, however, is 
relatively high: thus on a graph, the values of 
temperatures and pressure for ice lie above the 
vaporization curve, but do not extend to the 
right of 32°F (0°C) along the x-axis. To the right 
of 32°F, but above the vaporization curve, are the 
coordinates representing the temperature and 
pressure for water in its liquid state. 

Water has a number of unusual properties, 
one of which is its response to high pressures and 
low temperatures. If enough pressure is applied, 
it is possible to melt ice — thus transforming it 
from a solid to a liquid — at temperatures below 
the normal freezing point of 32°F. Thus, the line 
that divides solid on the left from liquid on the 
right is not exactly parallel to the y-axis: it slopes 
gradually toward the y-axis, meaning that at 
ultra-high pressures, water remains liquid even 
though it is well below the freezing point. 

Nonetheless, the line between solid and liq- 
uid has to intersect the vaporization curve some- 
where, and it does — at a coordinate slightly 
above freezing, but well below normal atmos- 
pheric pressure. This is the triple point, and 
though “common sense” might dictate that a 
thing cannot possibly be solid, liquid, and vapor 
all at once, a graph illustrating the triple point 
makes it clear how this can happen. 

Numbers 

In the above discussion — and indeed throughout 
this book — the existence of the decimal, or base- 

SCIENCE DF EVERYDAY THINGS 


Frame of 
Reference 



This Cartesian coordinate graph shows how a substance such as water could experience a triple 

POINT A POINT AT WHICH IT IS SIMULTANEOUSLY A LIQUID, A SOLID, AND A VAPOR. 


10, numeration system is taken for granted. Yet 
that system is a wonder unto itself, involving a 
complicated interplay of arbitrary and real val- 
ues. Though the value of the number 10 is 
absolute, the expression of it (and its use with 
other numbers) is relative to a frame of reference: 
one could just as easily use a base-12 system. 

Each numeration system has its own frame 
of reference, which is typically related to aspects 
of the human body. Thus throughout the course 
of history, some societies have developed a base- 
2 system based on the two hands or arms of a 
person. Others have used the fingers on one hand 
(base- 5) as their reference point, or all the fingers 
and toes (base-20). The system in use throughout 
most of the world today takes as its frame of ref- 
erence the ten fingers used for basic counting. 

□ □efficients. Numbers, of course, 
provide a means of assigning relative values to a 
variety of physical characteristics: length, mass, 
force, density, volume, electrical charge, and so 
on. In an expression such as “10 meters,” the 
numeral 10 is a coefficient, a number that serves 
as a measure for some characteristic or property. 
A coefficient may also be a factor against which 
other values are multiplied to provide a desired 
result. 

SCIENCE DF EVERYDAY THINGS 


For instance, the figure 3.141592, better 
known as pi (it), is a well-known coefficient used 
in formulae for measuring the circumference or 
area of a circle. Important examples of coeffi- 
cients in physics include those for static and slid- 
ing friction for any two given materials. A coeffi- 
cient is simply a number — not a value, as would 
be the case if the coefficient were a measure of 
something. 

Standards of Measurement 

Numbers and coefficients provide a convenient 
lead-in to the subject of measurement, a practical 
example of frame of reference in all sciences — 
and indeed, in daily life. Measurement always 
requires a standard of comparison: something 
that is fixed, against which the value of other 
things can be compared. A standard may be arbi- 
trary in its origins, but once it becomes fixed, it 
provides a frame of reference. 

Lines of longitude, for instance, are meas- 
ured against an arbitrary standard: the “Prime 
Meridian” running through Greenwich, England. 
An imaginary line drawn through that spot 
marks the line of reference for all longitudinal 
measures on Earth, with a value of 0°. There is 
nothing special about Greenwich in any pro- 
found scientific sense; rather, its place of impor- 

VDLUME 2: REAL-LIFE PHYSICS 


7 


Frame of 
Reference 


B 


tance reflects that of England itself, which ruled 
the seas and indeed much of the world at the 
time the Prime Meridian was established. 

The Equator, on the other hand, has a firm 
scientific basis as the standard against which all 
lines of latitude are measured. Yet today, the 
coordinates of a spot on Earth’s surface are given 
in relation to both the Equator and the Prime 
Meridian. 

c a l i b r at i □ n . Calibration is the 
process of checking and correcting the perform- 
ance of a measuring instrument or device against 
the accepted standard. America’s preeminent 
standard for the exact time of day, for instance, is 
the United States Naval Observatory in Washing- 
ton, D.C. Thanks to the Internet, people all over 
the country can easily check the exact time, and 
correct their clocks accordingly. 

There are independent scientific laboratories 
responsible for the calibration of certain instru- 
ments ranging from clocks to torque wrenches, 
and from thermometers to laser beam power 
analyzers. In the United States, instruments or 
devices with high-precision applications — that 
is, those used in scientific studies, or by high-tech 
industries — are calibrated according to standards 
established by the National Institute of Standards 
and Technology (NIST). 

THE VALUE DF STANDARD- 
IZATION to a society. Standardiza- 
tion of weights and measures has always been an 
important function of government. When Ch’in 
Shih-huang-ti (259-210 b.c.) united China for 
the first time, becoming its first emperor, he set 
about standardizing units of measure as a means 
of providing greater unity to the country — thus 
making it easier to rule. 

More than 2,000 years later, another 
empire — Russia — was negatively affected by its 
failure to adjust to the standards of technologi- 
cally advanced nations. The time was the early 
twentieth century, when Western Europe was 
moving forward at a rapid pace of industrializa- 
tion. Russia, by contrast, lagged behind — in part 
because its failure to adopt Western standards 
put it at a disadvantage. 

Train travel between the West and Russia 
was highly problematic, because the width of 
railroad tracks in Russia was different than in 
Western Europe. Thus, adjustments had to be 
performed on trains making a border crossing, 
and this created difficulties for passenger travel. 

vdlume z: real-life physics 


More importantly, it increased the cost of trans- 
porting freight from East to West. 

Russia also used the old Julian calendar, as 
opposed to the Gregorian calendar adopted 
throughout much of Western Europe after 1582. 
Thus October 25, 1917, in the Julian calendar of 
old Russia translated to November 7, 1917 in the 
Gregorian calendar used in the West. That date 
was not chosen arbitrarily: it was then that Com- 
munists, led by V. I. Lenin, seized power in the 
weakened former Russian Empire. 

METHODS OF DETERMINING 

s t a n d a r d s . It is easy to understand, 
then, why governments want to standardize 
weights and measures — as the U.S. Congress did 
in 1901, when it established the Bureau of Stan- 
dards (now NIST) as a nonregulatory agency 
within the Commerce Department. Today, NIST 
maintains a wide variety of standard definitions 
regarding mass, length, temperature, and so 
forth, against which other devices can be cali- 
brated. 

Note that NIST keeps on hand definitions 
rather than, say, a meter stick or other physical 
model. When the French government established 
the metric system in 1799, it calibrated the value 
of a kilogram according to what is now known as 
the International Prototype Kilogram, a plat- 
inum-iridium cylinder housed near Sevres in 
France. In the years since then, the trend has 
moved away from such physical expressions of 
standards, and toward standards based on a con- 
stant figure. Hence, the meter is defined as the 
distance light travels in a vacuum (an area of 
space devoid of air or other matter) during the 
interval of 1/299,792,458 of a second. 

metric vs. British. Scientists 
almost always use the metric system, not because 
it is necessarily any less arbitrary than the British 
or English system (pounds, feet, and so on), but 
because it is easier to use. So universal is the met- 
ric system within the scientific community that it 
is typically referred to simply as SI, an abbrevia- 
tion of the French Systeme International 
d’Unites — that is, “International System of 
Units.” 

The British system lacks any clear frame of 
reference for organizing units: there are 12 inch- 
es in a foot, but 3 feet in a yard, and 1,760 yards 
in a mile. Water freezes at 32°F instead of 0°, as it 
does in the Celsius scale associated with the met- 
ric system. In contrast to the English system, the 

science df everyday things 


metric system is neatly arranged according to the 
base- 10 numerical framework: 10 millimeters to 
a centimeter, 100 centimeters to a meter, 1,000 
meters to kilometer, and so on. 

The difference between the pound and the 
kilogram aptly illustrates the reason scientists in 
general, and physicists in particular, prefer the 
metric system. A pound is a unit of weight, 
meaning that its value is entirely relative to the 
gravitational pull of the planet on which it is 
measured. A kilogram, on the other hand, is a 
unit of mass, and does not change throughout 
the universe. Though the basis for a kilogram 
may not ultimately be any more fundamental 
than that for a pound, it measures a quality 
that — unlike weight — does not vary according to 
frame of reference. 

Frame of Reference in Clas- 
sical Physics and Astronomy 

Mass is a measure of inertia, the tendency of a 
body to maintain constant velocity. If an object is 
at rest, it tends to remain at rest, or if in motion, 
it tends to remain in motion unless acted upon 
by some outside force. This, as identified by the 
first law of motion, is inertia — and the greater 
the inertia, the greater the mass. 

Physicists sometimes speak of an “inertial 
frame of reference,” or one that has a constant 
velocity — that is, an unchanging speed and 
direction. Imagine if one were on a moving bus 
at constant velocity, regularly tossing a ball in the 
air and catching it. It would be no more difficult 
to catch the ball than if the bus were standing 
still, and indeed, there would be no way of deter- 
mining, simply from the motion of the ball itself, 
that the bus was moving. 

But what if the inertial frame of reference 
suddenly became a non-inertial frame of refer- 
ence — in other words, what if the bus slammed 
on its brakes, thus changing its velocity? While 
the bus was moving forward, the ball was moving 
along with it, and hence, there was no relative 
motion between them. By stopping, the bus 
responded to an “outside” force — that is, its 
brakes. The ball, on the other hand, experienced 
that force indirectly. Hence, it would continue to 
move forward as before, in accordance with its 
own inertia — only now it would be in motion 
relative to the bus. 

ASTRONOMY AND RELATIVE 

motion. The idea of relative motion plays a 

SCIENCE OF EVERYDAY THINGS 


powerful role in astronomy. At every moment, 
Earth is turning on its axis at about 1,000 MPH 
(1,600 km/h) and hurtling along its orbital path 
around the Sun at the rate of 67,000 MPH 
(107,826 km/h.) The fastest any human being — 
that is, the astronauts taking part in the Apollo 
missions during the late 1960s — has traveled is 
about 30% of Earth’s speed around the Sun. 

Yet no one senses the speed of Earth’s move- 
ment in the way that one senses the movement of 
a car — or indeed the way the astronauts per- 
ceived their speed, which was relative to the 
Moon and Earth. Of course, everyone experi- 
ences the results of Earth’s movement — the 
change from night to day, the precession of the 
seasons — but no one experiences it directly. It is 
simply impossible, from the human frame of ref- 
erence, to feel the movement of a body as large as 
Earth — not to mention larger progressions on 
the part of the Solar System and the universe. 

FROM ASTRDNDMY TD PHYS- 
ICS. The human body is in an inertial frame of 
reference with regard to Earth, and hence experi- 
ences no relative motion when Earth rotates or 
moves through space. In the same way, if one 
were traveling in a train alongside another train 
at constant velocity, it would be impossible to 
perceive that either train was actually moving — 
unless one referred to some fixed point, such as 
the trees or mountains in the background. Like- 
wise, if two trains were sitting side by side, and 
one of them started to move, the relative motion 
might cause a person in the stationary train to 
believe that his or her train was the one moving. 

For any measurement of velocity, and hence, 
of acceleration (a change in velocity), it is essen- 
tial to establish a frame of reference. Velocity and 
acceleration, as well as inertia and mass, figured 
heavily in the work of Galileo Galilei (1564- 
1642) and Sir Isaac Newton (1642-1727), both of 
whom may be regarded as “founding fathers” of 
modern physics. Before Galileo, however, had 
come Nicholas Copernicus (1473-1543), the first 
modern astronomer to show that the Sun, and 
not Earth, is at the center of “the universe” — 
by which people of that time meant the Solar 
System. 

In effect, Copernicus was saying that the 
frame of reference used by astronomers for mil- 
lennia was incorrect: as long as they believed 
Earth to be the center, their calculations were 
bound to be wrong. Galileo and later Newton, 

VDLUME 2: REAL-LIFE PHYSICS 


FRAME □ F 

Reference 


9 


Frame of 
Reference 


1 □ 


through their studies in gravitation, were able to 
prove Copernicus’s claim in terms of physics. 

At the same time, without the understanding 
of a heliocentric (Sun-centered) universe that he 
inherited from Copernicus, it is doubtful that 
Newton could have developed his universal law 
of gravitation. If he had used Earth as the center- 
point for his calculations, the results would have 
been highly erratic, and no universal law would 
have emerged. 

Relativity 

For centuries, the model of the universe devel- 
oped by Newton stood unchallenged, and even 
today it identifies the basic forces at work when 
speeds are well below that of the speed of light. 
However, with regard to the behavior of light 
itself — which travels at 186,000 mi (299,339 km) 
a second — Albert Einstein (1879-1955) began to 
observe phenomena that did not fit with New- 
tonian mechanics. The result of his studies was 
the Special Theory of Relativity, published in 
1905, and the General Theory of Relativity, pub- 
lished a decade later. Together these altered 
humanity’s view of the universe, and ultimately, 
of reality itself. 

Einstein himself once offered this charming 
explanation of his epochal theory: “Put your 
hand on a hot stove for a minute, and it seems 
like an hour. Sit with a pretty girl for an hour, and 
it seems like a minute. That’s relativity.” Of 
course, relativity is not quite as simple as that — 
though the mathematics involved is no more 
challenging than that of a high-school algebra 
class. The difficulty lies in comprehending how 
things that seem impossible in the Newtonian 
universe become realities near the speed of light. 

PLAYING TRICKS WITH TIME. 

An exhaustive explanation of relativity is far 
beyond the scope of the present discussion. What 
is important is the central precept: that no meas- 
urement of space or time is absolute, but depends 
on the relative motion of the observer (that is, 
the subject) and the observed (the object). Ein- 
stein further established that the movement of 
time itself is relative rather than absolute, a fact 
that would become apparent at speeds close to 
that of light. (His theory also showed that it is 
impossible to surpass that speed.) 

Imagine traveling on a spaceship at nearly 
the speed of light while a friend remains station- 

VDLUME z: real-life physics 


ary on Earth. Both on the spaceship and at the 
friend’s house on Earth, there is a TV camera 
trained on a clock, and a signal relays the image 
from space to a TV monitor on Earth, and vice 
versa. What the TV monitor reveals is surprising: 
from your frame of reference on the spaceship, it 
seems that time is moving more slowly for your 
friend on Earth than for you. Your friend thinks 
exactly the same thing — only, from the friend’s 
perspective, time on the spaceship is moving 
more slowly than time on Earth. How can this 
happen? 

Again, a full explanation — requiring refer- 
ence to formulae regarding time dilation, and so 
on — would be a rather involved undertaking. 
The short answer, however, is that which was 
stated above: no measurement of space or time is 
absolute, but each depends on the relative 
motion of the observer and the observed. Put 
another way, there is no such thing as absolute 
motion, either in the three dimensions of space, 
or in the fourth dimension identified by Ein- 
stein, time. All motion is relative to a frame of 
reference. 

RELATIVITY AND ITS IMPLICA- 
TIONS. The ideas involved in relativity have 
been verified numerous times, and indeed the 
only reason why they seem so utterly foreign to 
most people is that humans are accustomed to 
living within the Newtonian framework. Einstein 
simply showed that there is no universal frame of 
reference, and like a true scientist, he drew his 
conclusions entirely from what the data suggest- 
ed. He did not form an opinion, and only then 
seek the evidence to confirm it, nor did he seek to 
extend the laws of relativity into any realm 
beyond that which they described. 

Yet British historian Paul Johnson, in his 
unorthodox history of the twentieth century, 
Modern Times (1983; revised 1992), maintained 
that a world disillusioned by World War I saw a 
moral dimension to relativity. Describing a set of 
tests regarding the behavior of the Sun’s rays 
around the planet Mercury during an eclipse, 
the book begins with the sentence: “The modern 
world began on 29 May 1919, when photographs 
of a solar eclipse, taken on the Island of Principe 
off West Africa and at Sobral in Brazil, con- 
firmed the truth of a new theory of the uni- 
verse.” 

As Johnson went on to note, “...for most peo- 
ple, to whom Newtonian physics... were perfectly 

SCIENCE DF EVERYDAY THINGS 


Frame of 
Reference 


KEY TERMS 


absolute: Fixed; not dependent on 

anything else. The value of 10 is absolute, 
relating to unchanging numerical princi- 
ples; on the other hand, the value of 10 dol- 
lars is relative, reflecting the economy, 
inflation, buying power, exchange rates 
with other currencies, etc. 

calibration: The process of check- 

ing and correcting the performance of a 
measuring instrument or device against a 
commonly accepted standard. 

CARTESIAN COORDINATE SYSTEM: 

A method of specifying coordinates in rela- 
tion to an x-axis, y-axis, and z-axis. The 
system is named after the French mathe- 
matician and philosopher Rene Descartes 
(1596-1650), who first described its princi- 
ples, but it was developed greatly by French 
mathematician and philosopher Pierre de 
Fermat (1601-1665). 

coefficient: A number that serves 

as a measure for some characteristic or 
property. A coefficient may also be a factor 
against which other values are multiplied 
to provide a desired result. 

coordinate: A number or set of 

numbers used to specify the location of a 
point on a line, on a surface such as a 
plane, or in space. 


frame of reference: The per- 

spective of a subject in observing an object. 

object: Something that is perceived 

or observed by a subject. 

relative: Dependent on something 

else for its value or for other identifying 
qualities. The fact that the United States 
has a constitution is an absolute, but the 
fact that it was ratified in 1787 is relative: 
that date has meaning only within the 
Western calendar. 

subject: Something (usually a per- 

son) that perceives or observes an object 
and/or its behavior. 

x-axis: The horizontal line of refer- 

ence for points in the Cartesian coordinate 
system. 

y-axis: The vertical line of reference 

for points in the Cartesian coordinate sys- 
tem. 

z-axis: In a three-dimensional version 

of the Cartesian coordinate system, the z- 
axis is the line of reference for points in the 
third dimension. Typically the x-axis 
equates to “width,” the y-axis to “height,” 
and the z-axis to “depth” — though in fact 
length, width, and height are all relative to 
the observer’s frame of reference. 


comprehensible, relativity never became more 
than a vague source of unease. It was grasped that 
absolute time and absolute length had been 
dethroned.... All at once, nothing seemed certain 
in the spheres.... At the beginning of the 1920s the 
belief began to circulate, for the first time at a 
popular level, that there were no longer any 
absolutes: of time and space, of good and evil, of 
knowledge, above all of value. Mistakenly but 
perhaps inevitably, relativity became confused 
with relativism.” 

SCIENCE DF EVERYDAY THINGS 


Certainly many people agree that the twenti- 
eth century — an age that saw unprecedented 
mass murder under the dictatorships of Adolf 
Hitler and Josef Stalin, among others — was char- 
acterized by moral relativism, or the belief that 
there is no right or wrong. And just as Newton’s 
discoveries helped usher in the Age of Reason, 
when thinkers believed it was possible to solve 
any problem through intellectual effort, it is quite 
plausible that Einstein’s theory may have had this 
negative moral effect. 

VDLUME 2: REAL-LIFE PHYSICS 


1 1 



Frame of 
Reference 


If so, this was certainly not Einstein’s inten- 
tion. Aside from the fact that, as stated, he did not 
set out to describe anything other than the phys- 
ical behavior of objects, he continued to believe 
that there was no conflict between his ideas and a 
belief in an ordered universe: “Relativity,” he once 
said, “teaches us the connection between the dif- 
ferent descriptions of one and the same reality.” 

WHERE T □ LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Fleisher, Paul. Relativity and Quantum Mechanics: Princi- 
ples of Modern Physics. Minneapolis, MN: Lerner 
Publications, 2002. 

“Frame of Reference” (Web site). 

<http://www.physics.reading.ac.uk/units/flap/glos- 
sary/ff/frameref.html> (March 21, 2001). 


“Inertial Frame of Reference” (Web site). 

<http://id.mind.net/~zona/mstm/physics/mechan- 
ics/framesOfReference /inertialFrame.html> (March 
21 , 2001 ). 

Johnson, Paul. Modern Times: The World from the Twen- 
ties to the Nineties. Revised edition. New York: 
HarperPerennial, 1992. 

King, Andrew. Plotting Points and Position. Illustrated by 
Tony Kenyon. Brookfield, CT: Copper Beech Books, 
1998. 

Parker, Steve. Albert Einstein and Relativity. New York: 
Chelsea House, 1995. 

Robson, Pam. Clocks, Scales, and Measurements. New 
York: Gloucester Press, 1993. 

Rutherford, F. James; Gerald Holton; and Fletcher G. 
Watson. Project Physics. New York: Holt, Rinehart, 
and Winston, 1981. 

Swisher, Clarice. Relativity: Opposing Viewpoints. San 
Diego, CA: Greenhaven Press, 1990. 


1 2 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


KINEM AT ICS AND 

DYNAMICS 


C □ N C E PT 

Webster’s defines physics as “a science that deals 
with matter and energy and their interactions.” 
Alternatively, physics can be described as the 
study of matter and motion, or of matter inmo- 
tion. Whatever the particulars of the definition, 
physics is among the most fundamental of disci- 
plines, and hence, the rudiments of physics are 
among the most basic building blocks for think- 
ing about the world. Foundational to an under- 
standing of physics are kinematics, the explana- 
tion of how objects move, and dynamics, the 
study of why they move. Both are part of a larger 
branch of physics called mechanics, the study of 
bodies in motion. These are subjects that may 
sound abstract, but in fact, are limitless in their 
applications to real life. 

H □ W IT WORKS 

The Place of Physics in the 
Sciences 

Physics may be regarded as the queen of the sci- 
ences, not because it is “better” than chemistry or 
astronomy, but because it is the foundation on 
which all others are built. The internal and inter- 
personal behaviors that are the subject of the 
social sciences (psychology, anthropology, sociol- 
ogy, and so forth) could not exist without the 
biological framework that houses the human 
consciousness. Yet the human body and other 
elements studied by the biological and medical 
sciences exist within a larger environment, the 
framework for earth sciences, such as geology. 

Earth sciences belong to a larger grouping of 
physical sciences, each more fundamental in con- 
cerns and broader in scope. Earth, after all, is but 

SCIENCE □ F EVERYDAY THINGS 


one corner of the realm studied by astronomy; 
and before a universe can even exist, there must 
be interactions of elements, the subject of chem- 
istry. Yet even before chemicals can react, they 
have to do so within a physical framework — the 
realm of the most basic science — physics. 

The Birth eif Physics in 

□ REECE 

the first hypothesis. In- 
deed, physics stands in relation to the sciences as 
philosophy does to thought itself: without phi- 
losophy to provide the concept of concepts, it 
would be impossible to develop a consistent 
worldview in which to test ideas. It is no accident, 
then, that the founder of the physical sciences 
was also the world’s first philosopher, Thales (c. 
625?-547? b.c.) of Miletus in Greek Asia Minor 
(now part of Turkey.) Prior to Thales’s time, reli- 
gious figures and mystics had made statements 
regarding ethics or the nature of deity, but none 
had attempted statements concerning the funda- 
mental nature of reality. 

For instance, the Bible offers a story of 
Earth’s creation in the Book of Genesis which 
was well-suited to the understanding of people in 
the first millennium before Christ. But the writer 
of the biblical creation story made no attempt to 
explain how things came into being. He was con- 
cerned, rather, with showing that God had willed 
the existence of all physical reality by calling 
things into being — for example, by saying, “Let 
there be light.” 

Thales, on the other hand, made a genuine 
philosophical and scientific statement when he 
said that “Everything is water.” This was the first 
hypothesis, a statement capable of being scientif- 

VDLUME 2: REAL-LIFE PHYSICS 



MEASURE- 


Kinematics 

AN D 

DYNAMICS 


1 4 


ically tested for accuracy. Thales’s pronounce- 
ment did not mean he believed all things were 
necessarily made of water, literally. Rather, he 
appears to have been referring to a general ten- 
dency of movement: that the whole world is in a 
fluid state. 

ATTEMPTING TG UNDER- 

STAND PHYSICAL REALITY. While 

we can respect Thales’s statement for its truly 
earth-shattering implications, we may be tempted 
to read too much into it. Nonetheless, it is strik- 
ing that he compared physical reality to water. On 
the one hand, there is the fact that water is essen- 
tial to all life, and pervades Earth — but that is a 
subject more properly addressed by the realms of 
chemistry and the biological sciences. Perhaps of 
more interest to the physicist is the allusion to a 
fluid nature underlying all physical reality. 

The physical realm is made of matter, which 
appears in four states: solid, liquid, gas, and plas- 
ma. The last of these is not the same as blood 
plasma: containing many ionized atoms or mol- 
ecules which exhibit collective behavior, plasma 
is the substance from which stars, for instance, 
are composed. Though not plentiful on Earth, 
within the universe it may be the most common 
of all four states. Plasma is akin to gas, but differ- 
ent in molecular structure; the other three states 
differ at the molecular level as well. 

Nonetheless, it is possible for a substance 
such as water — genuine ld 2 0, not the figurative 
water of Thales — to exist in liquid, gas, or solid 
form, and the dividing line between these is not 
always fixed. In fact, physicists have identified a 
phenomenon known as the triple point: at a cer- 
tain temperature and pressure, a substance can 
be solid, liquid, and gas all at once! 

The above statement shows just how chal- 
lenging the study of physical reality can be, and 
indeed, these concepts would be far beyond the 
scope of Thales’s imagination, had he been pre- 
sented with them. Though he almost certainly 
deserves to be called a “genius,” he lived in a 
world that viewed physical processes as a product 
of the gods’ sometimes capricious will. The 
behavior of the tides, for instance, was attributed 
to Poseidon. Though Thales’s statement began 
the process of digging humanity out from under 
the burden of superstition that had impeded sci- 
entific progress for centuries, the road forward 
would be a long one. 

VDLUME 2: REAL-LIFE PHYSICS 


M AT HEM AT ICS, 

ment, and m att e r . In the two cen- 
turies after Thales’s death, several other thinkers 
advanced understanding of physical reality in 
one way or another. Pythagoras (c. 580-c. 500 
b.c.) taught that everything could be quantified, 
or related to numbers. Though he entangled this 
idea with mysticism and numerology, the con- 
cept itself influenced the idea that physical 
processes could be measured. Likewise, there 
were flaws at the heart of the paradoxes put forth 
by Zeno of Elea (c. 495-c. 430 b.c.), who set out 
to prove that motion was impossible — yet he was 
also the first thinker to analyze motion seriously. 

In one of Zeno’s paradoxes, he referred to an 
arrow being shot from a bow. At every moment 
of its flight, it could be said that the arrow was at 
rest within a space equal to its length. Though it 
would be some 2,500 years before slow-motion 
photography, in effect he was asking his listeners 
to imagine a snapshot of the arrow in flight. If it 
was at rest in that “snapshot,” he asked, so to 
speak, and in every other possible “snapshot,” 
when did the arrow actually move? These para- 
doxes were among the most perplexing questions 
of premodern times, and remain a subject of 
inquiry even today. 

In fact, it seems that Zeno unwittingly (for 
there is no reason to believe that he deliberately 
deceived his listeners) inserted an error in his 
paradoxes by treating physical space as though it 
were composed of an infinite number of points. 
In the ideal world of geometric theory, a point 
takes up no space, and therefore it is correct to 
say that a line contains an infinite number of 
points; but this is not the case in the real world, 
where a “point” has some actual length. Hence, if 
the number of points on Earth were limitless, so 
too would be Earth itself. 

Zeno’s contemporary Leucippus (c. 480-c. 
420 b.c.) and his student Democritus (c. 460-370 
b.c.) proposed a new and highly advanced model 
for the tiniest point of physical space: the atom. It 
would be some 2,300 years, however, before 
physicists returned to the atomic model. 

Aristotle’s Flawed Physics 

The study of matter and motion began to take 
shape with Aristotle (384-322 b.c.); yet, though 
his Physics helped establish a framework for the 
discipline, his errors are so profound that any 
praise must be qualified. Certainly, Aristotle was 

SCIENCE df everyday things 


Kinematics 

and 

Dynamics 


one of the world’s greatest thinkers, who origi- 
nated a set of formalized realms of study. How- 
ever, in Physics he put forth an erroneous expla- 
nation of matter and motion that still prevailed 
in Europe twenty centuries later. 

Actually, Aristotle’s ideas disappeared in the 
late ancient period, as learning in general came to 
a virtual halt in Europe. That his writings — 
which on the whole did much more to advance 
the progress of science than to impede it — sur- 
vived at all is a tribute to the brilliance of Arab, 
rather than European, civilization. Indeed, it was 
in the Arab world that the most important scien- 
tific work of the medieval period took place. 
Only after about 1200 did Aristotelian thinking 
once again enter Europe, where it replaced a 
crude jumble of superstitions that had been sub- 
stituted for learning. 

the f □ u r elements. Accord- 
ing to Aristotelian physics, all objects consisted, 
in varying degrees, of one or more elements: air, 
fire, water, and earth. In a tradition that went 
back to Thales, these elements were not necessar- 
ily pure: water in the everyday world was com- 
posed primarily of the element water, but also 
contained smaller amounts of the other ele- 
ments. The planets beyond Earth were said to be 
made up of a “fifth element,” or quintessence, of 
which little could be known. 

The differing weights and behaviors of the 
elements governed the behavior of physical 
objects. Thus, water was lighter than earth, for 
instance, but heavier than air or fire. It was due to 
this difference in weight, Aristotle reasoned, that 
certain objects fall faster than others: a stone, for 
instance, because it is composed primarily of 
earth, will fall much faster than a leaf, which has 
much less earth in it. 

Aristotle further defined “natural” motion as 
that which moved an object toward the center of 
the Earth, and “violent” motion as anything that 
propelled an object toward anything other than 
its “natural” destination. Hence, all horizontal or 
upward motion was “violent,” and must be the 
direct result of a force. When the force was 
removed, the movement would end. 

ARISTOTLE’S MODEL OF THE 

universe. From the fact that Earth’s cen- 
ter is the destination of all “natural” motion, it is 
easy to comprehend the Aristotelian cosmology, 
or model of the universe. Earth itself was in the 
center, with all other bodies (including the Sun) 

science of everyday things 




Aristotle. (The Bettmann Archive. Reproduced by permission.) 

revolving around it. Though in constant move- 
ment, these heavenly bodies were always in their 
“natural” place, because they could only move on 
the firmly established — almost groove-like — 
paths of their orbits around Earth. This in turn 
meant that the physical properties of matter and 
motion on other planets were completely differ- 
ent from the laws that prevailed on Earth. 

Of course, virtually every precept within the 
Aristotelian system is incorrect, and Aristotle 
compounded the influence of his errors by pro- 
moting a disdain for quantification. Specifically, 
he believed that mathematics had little value for 
describing physical processes in the real world, 
and relied instead on pure observation without 
attempts at measurement. 

Moving Beyond Aristotle 

Faulty as Aristotle’s system was, however, it pos- 
sessed great appeal because much of it seemed to 
fit with the evidence of the senses. It is not at all 
immediately apparent that Earth and the other 
planets revolve around the Sun, nor is it obvious 
that a stone and a leaf experience the same accel- 
eration as they fall toward the ground. In fact, 
quite the opposite appears to be the case: as 
everyone knows, a stone falls faster than a leaf. 
Therefore, it would seem reasonable — on the 

VDLUME 2: REAL-LIFE PHYSICS 


1 5 


Kinematics 
an D 

Dynamics 


i e 



Galileo. (Archive Photos, Inc. Reproduced by permission.) 

surface of it, at least — to accept Aristotle’s con- 
clusion that this difference results purely from a 
difference in weight. 

Today, of course, scientists — and indeed, 
even people without any specialized scientific 
knowledge — recognize the lack of merit in the 
Aristotelian system. The stone does fall faster 
than the leaf, but only because of air resistance, 
not weight. Hence, if they fell in a vacuum (a 
space otherwise entirely devoid of matter, includ- 
ing air), the two objects would fall at exactly the 
same rate. 

As with a number of truths about matter 
and motion, this is not one that appears obvious, 
yet it has been demonstrated. To prove this high- 
ly nonintuitive hypothesis, however, required an 
approach quite different from Aristotle’s — an 
approach that involved quantification and the 
separation of matter and motion into various 
components. This was the beginning of real 
progress in physics, and in a sense may be regard- 
ed as the true birth of the discipline. In the years 
that followed, understanding of physics would 
grow rapidly, thanks to advancements of many 
individuals; but their studies could not have been 
possible without the work of one extraordinary 
thinker who dared to question the Aristotelian 
model. 


REAL-LIFE 
A P P L I C AT I □ N S 

Kinematics: Haw Dbjects 
M qve 

By the sixteenth century, the Aristotelian world- 
view had become so deeply ingrained that few 
European thinkers would have considered the 
possibility that it could be challenged. Professors 
all over Europe taught Aristotle’s precepts to their 
students, and in this regard the University of Pisa 
in Italy was no different. Yet from its classrooms 
would emerge a young man who not only ques- 
tioned, but ultimately overturned the Aris- 
totelian model: Galileo Galilei (1564-1642.) 

Challenges to Aristotle had been slowly 
growing within the scientific communities of the 
Arab and later the European worlds during the 
preceding millennium. Yet the ideas that most 
influenced Galileo in his break with Aristotle 
came not from a physicist but from an 
astronomer, Nicolaus Copernicus (1473-1543.) It 
was Copernicus who made a case, based purely 
on astronomical observation, that the Sun and 
not Earth was at the center of the universe. 

Galileo embraced this model of the cosmos, 
but was later forced to renounce it on orders 
from the pope in Rome. At that time, of course, 
the Catholic Church remained the single most 
powerful political entity in Europe, and its 
endorsement of Aristotelian views — which 
philosophers had long since reconciled with 
Christian ideas — is a measure of Aristotle’s 
impact on thinking. 

GALILEO’S REVOLUTION IN 

physics. After his censure by the Church, 
Galileo was placed under house arrest and was 
forbidden to study astronomy. Instead he turned 
to physics — where, ironically, he struck the blow 
that would destroy the bankrupt scientific system 
endorsed by Rome. In 1638, he published Dis- 
courses and Mathematical Demonstrations Con- 
cerning Two New Sciences Pertaining to Mathe- 
matics and Local Motion, a work usually referred 
to as Two New Sciences. In it, he laid the ground- 
work for physics by emphasizing a new method 
that included experimentation, demonstration, 
and quantification of results. 

In this book — highly readable for a work of 
physics written in the seventeenth century — 
Galileo used a dialogue, an established format 
among philosophers and scientists of the past. 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



The character of Salviati argued for Galileo’s 
ideas and Simplicio for those of Aristotle, while 
the genial Sagredo sat by and made occasional 
comments. Through Salviati, Galileo chose to 
challenge Aristotle on an issue that to most peo- 
ple at the time seemed relatively settled: the claim 
that objects fall at differing speeds according to 
their weight. 

In order to proceed with his aim, Galileo had 
to introduce a number of innovations, and 
indeed, he established the subdiscipline of kine- 
matics, or how objects move. Aristotle had indi- 
cated that when objects fall, they fall at the same 
rate from the moment they begin to fall until 
they reach their “natural” position. Galileo, on 
the other hand, suggested an aspect of motion, 
unknown at the time, that became an integral 
part of studies in physics: acceleration. 

Scalars and Vectors 

Even today, many people remain confused as to 
what acceleration is. Most assume that accelera- 
tion means only an increase in speed, but in fact 
this represents only one of several examples of 
acceleration. Acceleration is directly related to 
velocity, often mistakenly identified with speed. 

In fact, speed is what scientists today would 
call a scalar quantity, or one that possesses mag- 
nitude but no specific direction. Speed is the rate 
at which the position of an object changes over a 
given period of time; thus people say “miles (or 
kilometers) per hour.” A story problem concern- 
ing speed might state that “A train leaves New 
York City at a rate of 60 miles (96.6 km/h). How 
far will it have traveled in 73 minutes?” 

Note that there is no reference to direction, 
whereas if the story problem concerned veloci- 
ty — a vector, that is, a quantity involving both 
magnitude and direction — it would include 
some crucial qualifying phrase after “New York 
City”: “for Boston,” perhaps, or “northward.” In 
practice, the difference between speed and veloc- 
ity is nearly as large as that between a math prob- 
lem and real life: few people think in terms of 
driving 60 miles, for instance, without also con- 
sidering the direction they are traveling. 

r e s u lt a nts. One can apply the 
same formula with velocity, though the process is 
more complicated. To obtain change in distance, 
one must add vectors, and this is best done by 
means of a diagram. You can draw each vector as 
an arrow on a graph, with the tail of each vector 

SCIENCE □ E EVERYDAY THINGS 


at the head of the previous one. Then it is possi- 
ble to draw a vector from the tail of the first to 
the head of the last. This is the sum of the vec- 
tors, known as a resultant, which measures the 
net change. 

Suppose, for instance, that a car travels east 4 
mi (6.44 km), then due north 3 mi (4.83 km). 
This may be drawn on a graph with four units 
along the x axis, then 3 units along the y axis, 
making two sides of a triangle. The number of 
sides to the resulting shape is always one more 
than the number of vectors being added; the final 
side is the resultant. From the tail of the first seg- 
ment, a diagonal line drawn to the head of the 
last will yield a measurement of 5 units — the 
resultant, which in this case would be equal to 5 
mi (8 km) in a northeasterly direction. 

VELOCITY AND ACCELERA- 
TION. The directional component of velocity 
makes it possible to consider forms of motion 
other than linear, or straight-line, movement. 
Principal among these is circular, or rotational 
motion, in which an object continually changes 
direction and thus, velocity. Also significant is 
projectile motion, in which an object is thrown, 
shot, or hurled, describing a path that is a combi- 
nation of horizontal and vertical components. 

Furthermore, velocity is a key component in 
acceleration, which is defined as a change in 
velocity. Hence, acceleration can mean one of five 
things: an increase in speed with no change in 
direction (the popular, but incorrect, definition 
of the overall concept); a decrease in speed with 
no change in direction; a decrease or increase of 
speed with a change in direction; or a change in 
direction with no change in speed. If a car speeds 
up or slows down while traveling in a straight 
line, it experiences acceleration. So too does an 
object moving in rotational motion, even if its 
speed does not change, because its direction will 
change continuously. 

Dynamics: Why Objects Move 

Galileo’s test. To return to 
Galileo, he was concerned primarily with a spe- 
cific form of acceleration, that which occurs due 
to the force of gravity. Aristotle had provided an 
explanation of gravity — if a highly flawed one — 
with his claim that objects fall to their “natural” 
position; Galileo set out to develop the first truly 
scientific explanation concerning how objects fall 
to the ground. 

VDLUME Z : REAL-LIFE PHYSICS 


KINEMATICS 

AND 

DYNAMICS 


1 7 


Kinematics 
an D 

Dynamics 


1 s 


According to Galileo’s predictions, two metal 
balls of differing sizes would fall with the same 
rate of acceleration. To test his hypotheses, how- 
ever, he could not simply drop two balls from a 
rooftop — or have someone else do so while he 
stood on the ground — and measure their rate of 
fall. Objects fall too fast, and lacking sophisticat- 
ed equipment available to scientists today, he had 
to find another means of showing the rate at 
which they fell. 

This he did by resorting to a method Aristo- 
tle had shunned: the use of mathematics as a 
means of modeling the behavior of objects. This 
is such a deeply ingrained aspect of science today 
that it is hard to imagine a time when anyone 
would have questioned it, and that very fact is a 
tribute to Galileo’s achievement. Since he could 
not measure speed, he set out to find an equation 
relating total distance to total time. Through a 
detailed series of steps, Galileo discovered that in 
uniform or constant acceleration from rest — that 
is, the acceleration he believed an object experi- 
ences due to gravity — there is a proportional 
relationship between distance and time. 

With this mathematical model, Galileo 
could demonstrate uniform acceleration. He did 
this by using an experimental model for which 
observation was easier than in the case of two 
falling bodies: an inclined plane, down which he 
rolled a perfectly round ball. This allowed him to 
extrapolate that in free fall, though velocity was 
greater, the same proportions still applied and 
therefore, acceleration was constant. 

POINTING THE WAY TOWARD 

newton. The effects of Galileo’s system were 
enormous: he demonstrated mathematically that 
acceleration is constant, and established a method 
of hypothesis and experiment that became the 
basis of subsequent scientific investigation. He 
did not, however, attempt to calculate a figure for 
the acceleration of bodies in free fall; nor did he 
attempt to explain the overall principle of gravity, 
or indeed why objects move as they do — the focus 
of a subdiscipline known as dynamics. 

At the end of Two New Sciences, Sagredo 
offered a hopeful prediction: “I really believe 
that... the principles which are set forth in this lit- 
tle treatise will, when taken up by speculative 
minds, lead to another more remarkable 
result....” This prediction would come true with 
the work of a man who, because he lived in a 
somewhat more enlightened time — and because 

VDLUME 2: REAL-LIFE PHYSICS 


he lived in England, where the pope had no 
power — was free to explore the implications of 
his physical studies without fear of Rome’s inter- 
vention. Born in the very year Galileo died, his 
name was Sir Isaac Newton (1642-1727.) 

NEWTON’S THREE LAWS OF 

motion. In discussing the movement of the 
planets, Galileo had coined the term inertia to 
describe the tendency of an object in motion to 
remain in motion, and an object at rest to remain 
at rest. This idea would be the starting point of 
Newton’s three laws of motion, and Newton 
would greatly expand on the concept of inertia. 

The three laws themselves are so significant 
to the understanding of physics that they are 
treated separately elsewhere in this volume; here 
they are considered primarily in terms of their 
implications regarding the larger topic of matter 
and motion. 

Introduced by Newton in his Principia 
(1687), the three laws are: 

• First law of motion: An object at rest will 
remain at rest, and an object in motion will 
remain in motion, at a constant velocity 
unless or until outside forces act upon it. 

• Second law of motion: The net force acting 
upon an object is a product of its mass mul- 
tiplied by its acceleration. 

• Third law of motion: When one object 
exerts a force on another, the second object 
exerts on the first a force equal in magni- 
tude but opposite in direction. 

These laws made final the break with Aristo- 
tle’s system. In place of “natural” motion, Newton 
presented the concept of motion at a uniform 
velocity — whether that velocity be a state of rest 
or of uniform motion. Indeed, the closest thing to 
“natural” motion (that is, true “natural” motion) 
is the behavior of objects in outer space. There, 
free from friction and away from the gravitation- 
al pull of Earth or other bodies, an object set in 
motion will remain in motion forever due to its 
own inertia. It follows from this observation, inci- 
dentally, that Newton’s laws were and are univer- 
sal, thus debunking the old myth that the physical 
properties of realms outside Earth are fundamen- 
tally different from those of Earth itself. 

MASS AND GRAVITATIONAL 

a c c e l e r at ion. The first law establishes 
the principle of inertia, and the second law makes 
reference to the means by which inertia is meas- 
ured: mass, or the resistance of an object to a 

science df everyday things 


Kinematics 

and 

Dynamics 


KEY TERMS 


accele rati □ n : A change in velocity. 

dynamics: The study of why objects 

move as they do; compare with kinematics. 

force: The product of mass multi- 

plied by acceleration. 

hypothesis: A statement capable of 

being scientifically tested for accuracy. 

i n e rti a: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

kinematics: The study of how 

objects move; compare with dynamics. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. 

matter: The material of physical real- 

ity. There are four basic states of matter: 
solid, liquid, gas, and plasma. 

mechanics: The study of bodies in 

motion. 

res u ltant: The sum of two or more 

vectors, which measures the net change in 
distance and direction. 


scalar: A quantity that possesses 

only magnitude, with no specific direction. 
Mass, time, and speed are all scalars. The 
opposite of a scalar is a vector. 

speed: The rate at which the position 

of an object changes over a given period of 
time. 

vacuum: Space entirely devoid of 

matter, including air. 

vector: A quantity that possesses 

both magnitude and direction. Velocity, 
acceleration, and weight (which involves 
the downward acceleration due to gravity) 
are examples of vectors. Its opposite is a 
scalar. 

ve lo c ity: The speed of an object in a 

particular direction. 

weight: A measure of the gravitation- 

al force on an object; the product of mass 
multiplied by the acceleration due to grav- 
ity. (The latter is equal to 32 ft or 9.8 m per 
second per second, or 32 ft/9.8 m per sec- 
ond squared.) 


change in its motion — including a change in 
velocity. Mass is one of the most fundamental 
notions in the world of physics, and it too is the 
subject of a popular misconception — one which 
confuses it with weight. In fact, weight is a force, 
equal to mass multiplied by the acceleration due 
to gravity. 

It was Newton, through a complicated series 
of steps he explained in his Principia, who made 
possible the calculation of that acceleration — an 
act of quantification that had eluded Galileo. The 
figure most often used for gravitational accelera- 
tion at sea level is 32 ft (9.8 m) per second 
squared. This means that in the first second, an 
object falls at a velocity of 32 ft per second, but its 

SCIENCE DF EVERYDAY THINGS 


velocity is also increasing at a rate of 32 ft per sec- 
ond per second. Hence, after 2 seconds, its veloc- 
ity will be 64 ft (per second; after 3 seconds 96 ft 
per second, and so on. 

Mass does not vary anywhere in the uni- 
verse, whereas weight changes with any change in 
the gravitational field. When United States astro- 
naut Neil Armstrong planted the American flag 
on the Moon in 1969, the flagpole (and indeed 
Armstrong himself) weighed much less than on 
Earth. Yet it would have required exactly the same 
amount of force to move the pole (or, again, 
Armstrong) from side to side as it would have on 
Earth, because their mass and therefore their 
inertia had not changed. 

VDLUME 2: REAL-LIFE PHYSICS 


1 9 



Kinematics 
an D 

Dynamics 


Beyond Mechanics 

The implications of Newton’s three laws go far 
beyond what has been described here; but again, 
these laws, as well as gravity itself, receive a much 
more thorough treatment elsewhere in this vol- 
ume. What is important in this context is the 
gradually unfolding understanding of matter and 
motion that formed the basis for the study of 
physics today. 

After Newton came the Swiss mathematician 
and physicist Daniel Bernoulli (1700-1782), who 
pioneered another subdiscipline, fluid dynamics, 
which encompasses the behavior of liquids and 
gases in contact with solid objects. Air itself is an 
example of a fluid, in the scientific sense of the 
term. Through studies in fluid dynamics, it 
became possible to explain the principles of air 
resistance that cause a leaf to fall more slowly 
than a stone — even though the two are subject to 
exactly the same gravitational acceleration, and 
would fall at the same speed in a vacuum. 

EXTENDING THE REALM DF 

physical study. The work of Galileo, 
Newton, and Bernoulli fit within one of five 
major divisions of classical physics: mechanics, 
or the study of matter, motion, and forces. The 
other principal divisions are acoustics, or studies 
in sound; optics, the study of light; thermody- 
namics, or investigations regarding the relation- 
ships between heat and other varieties of energy; 
and electricity and magnetism. (These subjects, 
and subdivisions within them, also receive exten- 
sive treatment elsewhere in this book.) 

Newton identified one type of force, gravita- 
tion, but in the period leading up to the time of 
Scottish physicist James Clerk Maxwell (1831- 
1879), scientists gradually became aware of a new 
fundamental interaction in the universe. Build- 
ing on studies of numerous scientists, Maxwell 
hypothesized that electricity and magnetism are 
in fact differing manifestations of a second vari- 
ety of force, electromagnetism. 

mddern physics. The term clas- 
sical physics, used above, refers to the subjects of 
study from Galileo’s time through the end of the 
nineteenth century. Classical physics deals pri- 
marily with subjects that can be discerned by the 
senses, and addressed processes that could be 
observed on a large scale. By contrast, modern 


physics, which had its beginnings with the work 
of Max Planck (1858-1947), Albert Einstein 
(1879-1955), Niels Bohr (1885-1962), and others 
at the beginning of the twentieth century, 
addresses quite a different set of topics. 

Modern physics is concerned primarily with 
the behavior of matter at the molecular, atomic, 
or subatomic level, and thus its truths cannot be 
grasped with the aid of the senses. Nor is classical 
physics much help in understanding modern 
physics. The latter, in fact, recognizes two forces 
unknown to classical physicists: weak nuclear 
force, which causes the decay of some subatomic 
particles, and strong nuclear force, which binds 
the nuclei of atoms with a force 1 trillion ( 10 12 ) 
times as great as that of the weak nuclear force. 

Things happen in the realm of modern 
physics that would have been inconceivable to 
classical physicists. For instance, according to 
quantum mechanics — first developed by 
Planck — it is not possible to make a measurement 
without affecting the object (e.g., an electron) 
being measured. Yet even atomic, nuclear, and par- 
ticle physics can be understood in terms of their 
effects on the world of experience: challenging as 
these subjects are, they still concern — though 
within a much more complex framework — the 
physical fundamentals of matter and motion. 

WHERE T □ LEARN MORE 

Ballard, Carol. How Do We Move? Austin, TX: Raintree 
Steck- Vaughn, 1998. 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Fleisher, Paul. Objects in Motion: Principles of Classical 
Mechanics. Minneapolis, MN: Lerner Publications, 
2002. 

Hewitt, Sally. Forces Around Us. New York: Children’s 
Press, 1998. 

Measure for Measure: Sites That Do the Work for You 
(Web site), <http://www.wolinskyweb.com/meas- 
ure.html> (March 7, 2001). 

Motion, Energy, and Simple Machines (Web site). 

<http://www.necc.mass.edu/MRVIS/MR3_13/start.ht 
ml> (March 7, 2001). 

Physlink.com (Web site), <http://www.physlink.com> 
(March 7, 2001). 

Rutherford, F. James; Gerald Holton; and Fletcher G. 
Watson. Project Physics. New York: Holt, Rinehart, 
and Winston, 1981. 

Wilson, Jerry D. Physics: Concepts and Applications, sec- 
ond edition. Lexington, MA: D. C. Heath, 1981. 


za 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 


DENSITY AND 


V □ L U M E 


C □ N C E PT 

Density and volume are simple topics, yet in 
order to work within any of the hard sciences, it 
is essential to understand these two types of 
measurement, as well as the fundamental quanti- 
ty involved in conversions between them — mass. 
Measuring density makes it possible to distin- 
guish between real gold and fake gold, and may 
also give an astronomer an important clue 
regarding the internal composition of a planet. 

H □ W IT WDRKS 

There are four fundamental standards by which 
most qualities in the physical world can be meas- 
ured: length, mass, time, and electric current. 
The volume of a cube, for instance, is a unit of 
length cubed: the length is multiplied by the 
width and multiplied by the height. Width and 
height, however, are not distinct standards of 
measurement: they are simply versions of length, 
distinguished by their orientation. Whereas 
length is typically understood as a distance along 
an x-axis in one-dimensional space, width adds a 
second dimension, and height a third. 

Of particular concern within this essay are 
length and mass, since volume is measured in 
terms of length, and density in terms of the ratio 
between mass and volume. Elsewhere in this 
book, the distinction between mass and weight 
has been presented numerous times from the 
standpoint of a person whose mass and weight are 
measured on Earth, and again on the Moon. Mass, 
of course, does not change, whereas weight does, 
due to the difference in gravitational force exerted 
by Earth as compared with that of its satellite, the 
Moon. But consider instead the role of the funda- 

SCIENCE □ F EVERYDAY THINGS 


mental quality, mass, in determining this signifi- 
cantly less fundamental property of weight. 

According to the second law of motion, 
weight is a force equal to mass multiplied by 
acceleration. Acceleration, in turn, is equal to 
change in velocity divided by change in time. 
Velocity, in turn, is equal to distance (a form of 
length) divided by time. If one were to express 
weight in terms of l, t, and m, with these repre- 
senting, respectively, the fundamental properties 
of length, time, and mass, it would be expressed as 

M • D 


— clearly, a much more complicated formu- 
la than that of mass! 

Mass 

So what is mass? Again, the second law of 
motion, derived by Sir Isaac Newton (1642- 
1727), is the key: mass is the ratio of force to 
acceleration. This topic, too, is discussed in 
numerous places throughout this book; what is 
actually of interest here is a less precise identifi- 
cation of mass, also made by Newton. 

Before formulating his laws of motion, New- 
ton had used a working definition of mass as the 
quantity of matter an object possesses. This is not 
of much value for making calculations or meas- 
urements, unlike the definition in the second law. 
Nonetheless, it serves as a useful reminder of 
matter’s role in the formula for density. 

Matter can be defined as a physical sub- 
stance not only having mass, but occupying 
space. It is composed of atoms (or in the case of 
subatomic particles, it is part of an atom), and is 

VDLUME 2: REAL-LIFE PHYSICS 


Density and 
Volume 



HOW DDES A GIGANTIC STEEL SHIP, SUCH AS THE SUPERTANKER PICTURED HERE, STAY AFLOAT, EVEN THOUGH IT 
HAS A WEIGHT DENSITY FAR GREATER THAN THE WATER BELOW IT? THE ANSWER LIES IN ITS CURVED HULL, WHICH 
CONTAINS A LARGE AMOUNT OF OPEN SPACE AND ALLOWS THE SHIP TO SPREAD ITS AVERAGE DENSITY TO A LOWER 

level than the water. (Photograph by Vince Streano/Corbis. Reproduced by permission.) 


22 


convertible with energy. The form or state of 
matter itself is not important: on Earth it is pri- 
marily observed as a solid, liquid, or gas, but it 
can also be found (particularly in other parts of 
the universe) in a fourth state, plasma. 

Yet there are considerable differences among 
types of matter — among various elements and 
states of matter. This is apparent if one imagines 
three gallon jugs, one containing water, the sec- 
ond containing helium, and the third containing 
iron filings. The volume of each is the same, but 
obviously, the mass is quite different. 

The reason, of course, is that at a molecular 
level, there is a difference in mass between the 
compound H 2 0 and the elements helium and 
iron. In the case of helium, the second-lightest of 
all elements after hydrogen, it would take a great 
deal of helium for its mass to equal that of iron. 
In fact, it would take more than 43,000 gallons of 
helium to equal the mass of the iron in one gal- 
lon jug! 

Density 

Rather than comparing differences in molecular 
mass among the three substances, it is easier to 
analyze them in terms of density, or mass divid- 

VDLUME 2: REAL-LIFE PHYSICS 


ed by volume. It so happens that the three items 
represent the three states of matter on Earth: liq- 
uid (water), solid (iron), and gas (helium). For 
the most part, solids tend to be denser than liq- 
uids, and liquids denser than gasses. 

One of the interesting things about density, 
as distinguished from mass and volume, is that it 
has nothing to do with the amount of material. A 
kilogram of iron differs from 10 kilograms of 
iron both in mass and volume, but the density of 
both samples is the same. Indeed, as discussed 
below, the known densities of various materials 
make it possible to determine whether a sample 
of that material is genuine. 

Volume 

Mass, because of its fundamental nature, is 
sometimes hard to comprehend, and density 
requires an explanation in terms of mass and vol- 
ume. Volume, on the other hand, appears to be 
quite straightforward — and it is, when one is 
describing a solid of regular shape. In other situ- 
ations, however, volume is more complicated. 

As noted earlier, the volume of a cube can be 
obtained simply by multiplying length by width 
by height. There are other means for measuring 

SCIENCE OF EVERYDAY THINGS 



Since scientists know Earth’s mass as well as its volume, they are easily able to compute its densi- 
ty — approximately 5 g/cm 3 . (Corbis. Reproduced by permission.) 


the volume of other straight-sided objects, such 
as a pyramid. That formula applies, indeed, for 
any polyhedron (a three-dimensional closed 
solid bounded by a set number of plane figures) 
that constitutes a modified cube in which the 
lengths of the three dimensions are unequal — 
that is, an oblong shape. 

For a cylinder or sphere, volume measure- 
ments can be obtained by applying formulae 
involving radius (r) and the constant n, roughly 
equal to 3. 14. The formula for volume of a cylinder 
is V = nr 2 h, where h is the height. A sphere’s volume 
can be obtained by the formula (4/3)7tr 3 . Even the 
volume of a cone can be easily calculated: it is one- 
third that of a cylinder of equal base and height. 

SCIENCE □ E EVERYDAY THINGS 


R E A L- L I F E 
A P P L I C AT I □ N S 

Measuring Volume 

What about the volume of a solid that is irregu- 
lar in shape? Some irregularly shaped objects, 
such as a scooter, which consists primarily of one 
round wheel and a number of oblong shapes, can 
be measured by separating them into regular 
shapes. Calculus may be employed with more 
complex problems to obtain the volume of an 
irregular shape — but the most basic method is 
simply to immerse the object in water. This pro- 
cedure involves measuring the volume of the 
water before and after immersion, and calculat- 
ing the difference. Of course, the object being 

VDLUME 2: REAL-LIFE PHYSICS 


23 




Density and 
Volume 


24 


measured cannot be water-soluble; if it is, its vol- 
ume must be measured in a non-water-based liq- 
uid such as alcohol. 

Measuring liquid volumes is easy, given the 
fact that liquids have no definite shape, and will 
simply take the shape of the container in which 
they are placed. Gases are similar to liquids in the 
sense that they expand to fit their container; 
however, measurement of gas volume is a more 
involved process than that used to measure either 
liquids or solids, because gases are highly respon- 
sive to changes in temperature and pressure. 

If the temperature of water is raised from its 
freezing point to its boiling point (32° to 212°F or 
0 to 100°C), its volume will increase by only 2%. 
If its pressure is doubled from 1 atm (defined as 
normal air pressure at sea level — 14.7 pounds- 
per-square-inch or 1.013 x 10 5 Pa) to 2 atm, vol- 
ume will decrease by only 0.01%. 

Yet, if air were heated from 32° to 212°F, its 
volume would increase by 37%; and if its pres- 
sure were doubled from 1 atm to 2, its volume 
would decrease by 50%. Not only do gases 
respond dramatically to changes in temperature 
and pressure, but also, gas molecules tend to be 
non-attractive toward one another — that is, they 
do not tend to stick together. Hence, the concept 
of “volume” involving gas is essentially meaning- 
less, unless its temperature and pressure are 
known. 

Buoyancy: Volume and 
Density 

Consider again the description above, of an 
object with irregular shape whose volume is 
measured by immersion in water. This is not the 
only interesting use of water and solids when 
dealing with volume and density. Particularly 
intriguing is the concept of buoyancy expressed 
in Archimedes’s principle. 

More than twenty-two centuries ago, the 
Greek mathematician, physicist, and inventor 
Archimedes (c. 287-212 b.c.) received orders 
from the king of his hometown — Syracuse, a 
Greek colony in Sicily — to weigh the gold in the 
royal crown. According to legend, it was while 
bathing that Archimedes discovered the principle 
that is today named after him. He was so excited, 
legend maintains, that he jumped out of his bath 

VDLUME 2: REAL-LIFE PHYSICS 


and ran naked through the streets of Syracuse 
shouting “Eureka!” (I have found it). 

What Archimedes had discovered was, in 
short, the reason why ships float: because the 
buoyant, or lifting, force of an object immersed 
in fluid is equal to the weight of the fluid dis- 
placed by the object. 

H □ W A STEEL SHIP FLOATS 

on water. Today most ships are made of 
steel, and therefore, it is even harder to under- 
stand why an aircraft carrier weighing many 
thousands of tons can float. After all, steel has a 
weight density (the preferred method for meas- 
uring density according to the British system of 
measures) of 480 pounds per cubic foot, and a 
density of 7,800 kilograms-per-cubic-meter. By 
contrast, sea water has a weight density of 64 
pounds per cubic foot, and a density of 1,030 
kilograms-per-cubic-meter. 

This difference in density should mean that 
the carrier would sink like a stone — and indeed it 
would, if all the steel in it were hammered flat. As 
it is, the hull of the carrier (or indeed of any sea- 
worthy ship) is designed to displace or move a 
quantity of water whose weight is greater than 
that of the vessel itself. The weight of the displaced 
water — that is, its mass multiplied by the down- 
ward acceleration due to gravity — is equal to the 
buoyant force that the ocean exerts on the ship. If 
the ship weighs less than the water it displaces, it 
will float; but if it weighs more, it will sink. 

Put another way, when the ship is placed in 
the water, it displaces a certain quantity of water 
whose weight can be expressed in terms of Vdg — 
volume multiplied by density multiplied by the 
downward acceleration due to gravity. The densi- 
ty of sea water is a known figure, as is g (32 ft or 
9.8 m/sec 2 ); thus the only variable for the water 
displaced is its volume. 

For the buoyant force on the ship, g will of 
course be the same, and the value of V will be the 
same as for the water. In order for the ship to 
float, then, its density must be much less than 
that of the water it has displaced. This can be 
achieved by designing the ship in order to maxi- 
mize displacement. The steel is spread over as 
large an area as possible, and the curved hull, 
when seen in cross section, contains a relatively 
large area of open space. Obviously, the density 
of this space is much less than that of water; thus, 
the average density of the ship is greatly reduced, 
which enables it to float. 

SCIENCE OF EVERYDAY THINGS 


Density and 
Volume 


KEY TERMS 


ARCHIMEDES’S PRINCIPLE: A rule 

of physics which holds that the buoyant 
force of an object immersed in fluid is 
equal to the weight of the fluid displaced 
by the object. It is named after the Greek 
mathematician, physicist, and inventor 
Archimedes (c. 287-212 b.c.), who first 
identified it. 

buoyancy: The tendency of an object 

immersed in a fluid to float. This can be 
explained by Archimedes’s principle. 

density: The ratio of mass to vol- 

ume — in other words, the amount of mat- 
ter within a given area. 

mass: According to the second law of 

motion, mass is the ratio of force to acceler- 
ation. Mass may likewise be defined, though 
much less precisely, as the amount of mat- 
ter an object contains. Mass is also the 
product of volume multiplied by density. 

matter: Physical substance that occu- 

pies space, has mass, is composed of atoms 
(or in the case of subatomic particles, is 


part of an atom), and is convertible into 
energy. 

specific gravity: The density of 

an object or substance relative to the densi- 
ty of water; or more generally, the ratio 
between the densities of two objects or 
substances. 

vdlume: The amount of three- 

dimensional space an object occupies. Vol- 
ume is usually expressed in cubic units of 
length. 

weight density: The proper term 

for density within the British system of 
weights and measures. The pound is a unit 
of weight rather than of mass, and thus 
British units of density are usually ren- 
dered in terms of weight density — that is, 
pounds-per-cubic-foot. By contrast, the 
metric or international units measure mass 
density (referred to simply as “density”), 
which is rendered in terms of kilograms- 
per-cubic-meter, or grams-per-cubic- 
centimeter. 


Comparing Densities 

As noted several times, the densities of numerous 
materials are known quantities, and can be easily 
compared. Some examples of density, all 
expressed in terms of kilograms per cubic meter, 
are: 

• Hydrogen: 0.09 kg/m 3 

• Air: 1.3 kg/m 3 

• Oak: 720 kg/m 3 

• Ethyl alcohol: 790 kg/m 3 

• Ice: 920 kg/m 3 

• Pure water: 1,000 kg/m 3 

• Concrete: 2,300 kg/m 3 

• Iron and steel: 7,800 kg/m 3 

• Lead: 11,000 kg/m 3 

• Gold: 19,000 kg/m 3 

SCIENCE DF EVERYDAY THINGS 


Note that pure water (as opposed to sea 
water, which is 3% denser) has a density of 1,000 
kilograms per cubic meter, or 1 gram per cubic 
centimeter. This value is approximate; however, 
at a temperature of 39.2°F (4°C) and under nor- 
mal atmospheric pressure, it is exact, and so, 
water is a useful standard for measuring the spe- 
cific gravity of other substances. 

SPECIFIC GRAVITY AND THE 

densities df planets. Specific 
gravity is the ratio between the densities of two 
objects or substances, and it is expressed as a 
number without units of measure. Due to the 
value of 1 g/cm 3 for water, it is easy to determine 
the specific gravity of a given substance, which 
will have the same number value as its density. 
For example, the specific gravity of concrete, 
which has a density of 2.3 g/cm 3 , is 2.3. The spe- 

VDLUME z: REAL-LIFE PHYSICS 


25 



Density and 
Volume 


cific gravities of gases are usually determined in 
comparison to the specific gravity of dry air. 

Most rocks near the surface of Earth have a 
specific gravity of somewhere between 2 and 3, 
while the specific gravity of the planet itself is 
about 5. How do scientists know that the density 
of Earth is around 5 g/cm 3 ? The computation is 
fairly simple, given the fact that the mass and vol- 
ume of the planet are known. And given the fact 
that most of what lies close to Earth’s surface — 
sea water, soil, rocks — has a specific gravity well 
below 5, it is clear that Earth’s interior must con- 
tain high-density materials, such as nickel or 
iron. In the same way, calculations regarding the 
density of other objects in the Solar System pro- 
vide a clue as to their interior composition. 

ALL T H AT G L I TT E R S . Closer tO 

home, a comparison of density makes it possible 
to determine whether a piece of jewelry alleged 
to be solid gold is really genuine. To determine 
the answer, one must drop it in a beaker of water 
with graduated units of measure clearly marked. 
(Here, figures are given in cubic centimeters, 
since these are easiest to use in this context.) 

Suppose the item has a mass of 10 grams. 
The density of gold is 19 g/cm 3 , and since V = 
mid = 10/19, the volume of water displaced by 
the gold should be 0.53 cm 3 . Suppose that 
instead, the item displaced 0.91 cm 3 of water. 
Clearly, it is not gold, but what is it? 

Given the figures for mass and volume, its 
density would be equal to m/V = 10/0.91 = 11 
g/cm 3 — which happens to be the density of lead. 
If on the other hand the amount of water dis- 
placed were somewhere between the values for 


pure gold and pure lead, one could calculate 
what portion of the item was gold and which 
lead. It is possible, of course, that it could contain 
some other metal, but given the high specific 
gravity of lead, and the fact that its density is rel- 
atively close to that of gold, lead is a favorite gold 
substitute among jewelry counterfeiters. 

WHERE TEI LEARN M El R E 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Science 
for Curious Minds. Illustrated by Ann Humphrey 
Williams. Hauppauge, N.Y.: Barron’s, 2000. 

“Density and Specific Gravity” (Web site). 

<http://www.tpub.com/fluid/chle.htm> (March 27, 
2001). 

“Density, Volume, and Cola” (Web site). 

<http://student.biology.arizona.edu/sciconn/densi- 
ty/density_coke.html> (March 27, 2001). 

“The Mass Volume Density Challenge” (Web site). 
<http://science-math-technology.com/mass_vol- 
ume_density.html> (March 27, 2001). 

“Metric Density and Specific Gravity” (Web site). 

<http://www.essexl .com/ people/speer/ density.html> 
(March 27, 2001). 

“Mineral Properties: Specific Gravity” The Mineral and 
Gemstone Kingdom (Web site), <http://www.mmer- 
als.net/resource/property/sg.htm> (March 27, 2001). 

Robson, Pam. Clocks, Scales and Measurements. New 
York: Gloucester Press, 1993. 

“Volume, Mass, and Density” (Web site). 

<http://www.nyu.edu/pages/mathmol/modules/water 
/density_intro.html> (March 27, 2001). 

Willis, Shirley. Tell Me Flow Ships Float. Illustrated by the 
author. New York: Franklin Watts, 1999. 


26 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


□ □ N S E R VAT I □ N 


LAWS 


C □ N C E PT 

The term “conservation laws” might sound at 
first like a body of legal statutes geared toward 
protecting the environment. In physics, however, 
the term refers to a set of principles describing 
certain aspects of the physical universe that are 
preserved throughout any number of reactions 
and interactions. Among the properties con- 
served are energy, linear momentum, angular 
momentum, and electrical charge. (Mass, too, is 
conserved, though only in situations well below 
the speed of light.) The conservation of these 
properties can be illustrated by examples as 
diverse as dropping a ball (energy); the motion of 
a skater spinning on ice (angular momentum); 
and the recoil of a rifle (linear momentum). 

H □ W IT WDRKS 

The conservation laws describe physical proper- 
ties that remain constant throughout the various 
processes that occur in the physical world. In 
physics, “to conserve” something means “to result 
in no net loss of” that particular component. For 
each such component, the input is the same as 
the output: if one puts a certain amount of ener- 
gy into a physical system, the energy that results 
from that system will be the same as the energy 
put into it. 

The energy may, however, change forms. In 
addition, the operations of the conservation laws 
are — on Earth, at least — usually affected by a 
number of other forces, such as gravity, friction, 
and air resistance. The effects of these forces, 
combined with the changes in form that take 
place within a given conserved property, some- 
times make it difficult to perceive the working of 
the conservation laws. It was stated above that 

SCIENCE □ F EVERYDAY THINGS 


the resulting energy of a physical system will be 
the same as the energy that was introduced to it. 
Note, however, that the usable energy output of a 
system will not be equal to the energy input. This 
is simply impossible, due to the factors men- 
tioned above — particularly friction. 

When one puts gasoline into a motor, for 
instance, the energy that the motor puts out will 
never be as great as the energy contained in the 
gasoline, because part of the input energy is 
expended in the operation of the motor itself. 
Similarly, the angular momentum of a skater on 
ice will ultimately be dissipated by the resistant 
force of friction, just as that of a Frisbee thrown 
through the air is opposed both by gravity and 
air resistance — itself a specific form of friction. 

In each of these cases, however, the property 
is still conserved, even if it does not seem so to 
the unaided senses of the observer. Because the 
motor has a usable energy output less than the 
input, it seems as though energy has been lost. In 
fact, however, the energy has only changed forms, 
and some of it has been diverted to areas other 
than the desired output. (Both the noise and the 
heat of the motor, for instance, represent uses of 
energy that are typically considered undesirable.) 
Thus, upon closer study of the motor — itself an 
example of a system — it becomes clear that the 
resulting energy, if not the desired usable output, 
is the same as the energy input. 

As for the angular momentum examples in 
which friction, or air resistance, plays a part, here 
too (despite all apparent evidence to the con- 
trary) the property is conserved. This is easier to 
understand if one imagines an object spinning in 
outer space, free from the opposing force of fric- 
tion. Thanks to the conservation of angular 

VDLUME Z: REAL-LIFE PHYSICS 


Z7 




AS THIS HUNTER FIRES HIS RIFLE, THE RIFLE PRODUCES A BACKWARD “KICK” AGAINST HIS SHOULDER. THIS KICK, 
WITH A VELOCITY IN THE OPPOSITE DIRECTION OF THE BULLET’S TRAJECTORY, HAS A MOMENTUM EXACTLY THE SAME 

as that of the bullet itself: hence momentum is conserved. (Photograph by Tony Arruza/Corbis. Reproduced by 
permission.) 


ZB 


momentum, an object set into rotation in space 
will continue to spin indefinitely. Thus, if an 
astronaut in the 1960s, on a spacewalk from his 
capsule, had set a screwdriver spinning in the 
emptiness of the exosphere, the screwdriver 
would still be spinning today! 

Energy and Mass 

Among the most fundamental statements in all 
of science is the conservation of energy: a system 
isolated from all outside factors will maintain the 
same total amount of energy, even though ener- 
gy transformations from one form or another 
take place. 

Energy is manifested in many varieties, 
including thermal, electromagnetic, sound, 
chemical, and nuclear energy, but all these are 
merely reflections of three basic types of energy. 
There is potential energy, which an object pos- 
sesses by virtue of its position; kinetic energy, 
which it possesses by virtue of its motion; and 
rest energy, which it possesses by virtue of its 
mass. 

The last of these three will be discussed in 
the context of the relationship between energy 
and mass; at present the concern is with potential 

VDLUME 2: REAL-LIFE PHYSICS 


and kinetic energy. Every system possesses a cer- 
tain quantity of both, and the sum of its poten- 
tial and kinetic energy is known as mechanical 
energy. The mechanical energy within a system 
does not change, but the relative values of poten- 
tial and kinetic energy may be altered. 

A SIMPLE EXAMPLE DF ME- 
CHANICAL energy. If one held a base- 
ball at the top of a tall building, it would have a 
certain amount of potential energy. Once it was 
dropped, it would immediately begin losing 
potential energy and gaining kinetic energy pro- 
portional to the potential energy it lost. The rela- 
tionship between the two forms, in fact, is 
inverse: as the value of one variable decreases, 
that of the other increases in exact proportion. 

The ball cannot keep falling forever, losing 
potential energy and gaining kinetic energy. In 
fact, it can never gain an amount of kinetic ener- 
gy greater than the potential energy it possessed 
in the first place. At the moment before it hits the 
ground, the ball’s kinetic energy is equal to the 
potential energy it possessed at the top of the 
building. Correspondingly, its potential energy is 
zero — the same amount of kinetic energy it pos- 
sessed before it was dropped. 

SCIENCE OF EVERYDAY THINGS 


Then, as the ball hits the ground, the energy 
is dispersed. Most of it goes into the ground, and 
depending on the rigidity of the ball and the 
ground, this energy may cause the ball to bounce. 
Some of the energy may appear in the form of 
sound, produced as the ball hits bottom, and 
some will manifest as heat. The total energy, 
however, will not be lost: it will simply have 
changed form. 

rest energy. The values for 
mechanical energy in the above illustration 
would most likely be very small; on the other 
hand, the rest or mass energy of the baseball 
would be staggering. Given the weight of 0.333 
pounds for a regulation baseball, which on Earth 
converts to 0.15 kg in mass, it would possess 
enough energy by virtue of its mass to provide a 
year’s worth of electrical power to more than 
150,000 American homes. This leads to two obvi- 
ous questions: how can a mere baseball possess 
all that energy? And if it does, how can the ener- 
gy be extracted and put to use? 

The answer to the second question is, “By 
accelerating it to something close to the speed of 
light” — which is more than 27,000 times faster 
than the fastest speed ever achieved by humans. 
(The astronauts on Apollo 10 in May 1969 
reached nearly 25,000 MPH (40,000 km/h), 
which is more than 33 times the speed of sound 
but still insignificant when compared to the 
speed of light.) The answer to the first question 
lies in the most well-known physics formula of 
all time: E = me 2 

In 1905, Albert Einstein (1879-1955) pub- 
lished his Special Theory of Relativity, which he 
followed a decade later with his General Theory 
of Relativity. These works introduced the world 
to the above-mentioned formula, which holds 
that energy is equal to mass multiplied by the 
squared speed of light. This formula gained its 
widespread prominence due to the many impli- 
cations of Einstein’s Relativity, which quite liter- 
ally changed humanity’s perspective on the uni- 
verse. Most concrete among those implications 
was the atom bomb, made possible by the un- 
derstanding of mass and energy achieved by 
Einstein. 

In fact, E = me 2 is the formula for rest ener- 
gy, sometimes called mass energy. Though rest 
energy is “outside” of kinetic and potential ener- 
gy in the sense that it is not defined by the above- 
described interactions within the larger system of 



As Surya Bonaly goes into a spin on the ice, she 

DRAWS IN HER ARMS AND LEG, REDUCING THE MOMENT 

of inertia. Because of the conservation of angu- 
lar MOMENTUM, HER ANGULAR VELOCITY WILL 
INCREASE, MEANING THAT SHE WILL SPIN MUCH FASTER. 

(Bolemian Nomad Picturemakers/Corbis. Reproduced by permission.) 

mechanical energy, its relation to the other forms 
can be easily shown. All three are defined in 
terms of mass. Potential energy is equal to mgh, 
where m is mass, g is gravity, and h is height. 
Kinetic energy is equal to / mv 2 , where v is veloc- 
ity. In fact — using a series of steps that will not be 
demonstrated here — it is possible to directly 
relate the kinetic and rest energy formulae. 

The kinetic energy formula describes the 
behavior of objects at speeds well below the 
speed of light, which is 186,000 mi (297,600 km) 
per second. But at speeds close to that of the 
speed of light, / mv 2 does not accurately reflect 
the energy possessed by the object. For instance, 
if v were equal to 0.999c (where c represents the 
speed of light), then the application of the for- 
mula A mv 2 would yield a value equal to less than 
3% of the object’s real energy. In order to calcu- 
late the true energy of an object at 0.999c, it 
would be necessary to apply a different formula 
for total energy, one that takes into account the 
fact that, at such a speed, mass itself becomes 
energy. 


Conservation 

Laws 


29 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


Conservation 

Laws 


CONSERVATION OF MASS. 

Mass itself is relative at speeds approaching c, 
and, in fact, becomes greater and greater the clos- 
er an object comes to the speed of light. This may 
seem strange in light of the fact that there is, after 
all, a law stating that mass is conserved. But mass 
is only conserved at speeds well below c: as an 
object approaches 186,000 mi (297,600 km) per 
second, the rules are altered. 

The conservation of mass states that total 
mass is constant, and is unaffected by factors 
such as position, velocity, or temperature, in any 
system that does not exchange any matter with its 
environment. Yet, at speeds close to c, the mass of 
an object increases dramatically. 

In such a situation, the mass would be equal 
to the rest, or starting mass, of the object divided 
by V(1 - (v 2 /c 2 ), where v is the object’s speed of 
relative motion. The denominator of this equa- 
tion will always be less than one, and the greater 
the value of v, the smaller the value of the 
denominator. This means that at a speed of c, the 
denominator is zero — in other words, the 
object’s mass is infinite! Obviously, this is not 
possible, and indeed, what the formula actually 
shows is that no object can travel faster than the 
speed of light. 

Of particular interest to the present discus- 
sion, however, is the fact, established by relativity 
theory, that mass can be converted into energy. 
Hence, as noted earlier, a baseball or indeed any 
object can be converted into energy — and since 
the formula for rest energy requires that the mass 
be multiplied by c 2 , clearly, even an object of vir- 
tually negligible mass can generate a staggering 
amount of energy. This conversion of mass to 
energy happens well below the speed of light, in 
a very small way, when a stick of dynamite 
explodes. A portion of that stick becomes energy, 
and the fact that this portion is equal to just 6 
parts out of 100 billion indicates the vast propor- 
tions of energy available from converted mass. 

□ ther Conservation Laws 

In addition to the conservation of energy, as well 
as the limited conservation of mass, there are 
laws governing the conservation of momentum, 
both for an object in linear (straight-line) 
motion, and for one in angular (rotational) 
motion. Momentum is a property that a moving 
body possesses by virtue of its mass and velocity, 
which determines the amount of force and time 


required to stop it. Linear momentum is equal to 
mass multiplied by velocity, and the conservation 
of linear momentum law states that when the 
sum of the external force vectors acting on a 
physical system is equal to zero, the total linear 
momentum of the system remains unchanged, or 
conserved. 

Angular momentum, or the momentum of 
an object in rotational motion, is equal to mr 2 co, 
where m is mass, r is the radius of rotation, and 
CO (the Greek letter omega) stands for angular 
velocity. According to the conservation of angu- 
lar momentum law, when the sum of the external 
torques acting on a physical system is equal to 
zero, the total angular momentum of the system 
remains unchanged. Torque is a force applied 
around an axis of rotation. When playing the old 
game of “spin the bottle,” for instance, one is 
applying torque to the bottle and causing it to 
rotate. 

electric charge. The conser- 
vation of both linear and angular momentum are 
best explained in the context of real-life exam- 
ples, provided below. Before going on to those 
examples, however, it is appropriate here to dis- 
cuss a conservation law that is outside the realm 
of everyday experience: the conservation of elec- 
tric charge, which holds that for an isolated sys- 
tem, the net electric charge is constant. 

This law is “outside the realm of everyday 
experience” such that one cannot experience it 
through the senses, but at every moment, it is 
happening everywhere. Every atom has positive- 
ly charged protons, negatively charged electrons, 
and uncharged neutrons. Most atoms are neu- 
tral, possessing equal numbers of protons and 
electrons; but, as a result of some disruption, an 
atom may have more protons than electrons, and 
thus, become positively charged. Conversely, it 
may end up with a net negative charge due to a 
greater number of electrons. But the protons or 
electrons it released or gained did not simply 
appear or disappear: they moved from one part 
of the system to another — that is, from one atom 
to another atom, or to several other atoms. 

Throughout these changes, the charge of 
each proton and electron remains the same, and 
the net charge of the system is always the sum of 
its positive and negative charges. Thus, it is 
impossible for any electrical charge in the uni- 
verse to be smaller than that of a proton or elec- 
tron. Likewise, throughout the universe, there is 


3D 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


always the same number of negative and positive 
electrical charges: just as energy changes form, 
the charges simply change position. 

There are also conservation laws describing 
the behavior of subatomic particles, such as the 
positron and the neutrino. However, the most 
significant of the conservation laws are those 
involving energy (and mass, though with the lim- 
itations discussed above), linear momentum, 
angular momentum, and electrical charge. 

REAL-LIFE 
A P P L I C AT IONS 

Conservation of Linear 
Momentum: Rifles and 
Rockets 

firing a rifle. The conservation 
of linear momentum is reflected in operations as 
simple as the recoil of a rifle when it is fired, and 
in those as complex as the propulsion of a rocket 
through space. In accordance with the conserva- 
tion of momentum, the momentum of a system 
must be the same after it undergoes an operation 
as it was before the process began. Before firing, 
the momentum of a rifle and bullet is zero, and 
therefore, the rifle-bullet system must return to 
that same zero-level of momentum after it is 
fired. Thus, the momentum of the bullet must be 
matched — and “cancelled” within the system 
under study — by a corresponding backward 
momentum. 

When a person shooting a gun pulls the trig- 
ger, it releases the bullet, which flies out of the 
barrel toward the target. The bullet has mass and 
velocity, and it clearly has momentum; but this is 
only half of the story. At the same time it is fired, 
the rifle produces a “kick,” or sharp jolt, against 
the shoulder of the person who fired it. This 
backward kick, with a velocity in the opposite 
direction of the bullet’s trajectory, has a momen- 
tum exactly the same as that of the bullet itself: 
hence, momentum is conserved. 

But how can the rearward kick have the 
same momentum as that of the bullet? After all, 
the bullet can kill a person, whereas, if one holds 
the rifle correctly, the kick will not even cause any 
injury. The answer lies in several properties of 
linear momentum. First of all, as noted earlier, 
momentum is equal to mass multiplied by veloc- 
ity; the actual proportions of mass and velocity, 


however, are not important as long as the back- 
ward momentum is the same as the forward 
momentum. The bullet is an object of relatively 
small mass and high velocity, whereas the rifle is 
much larger in mass, and hence, its rearward 
velocity is correspondingly small. 

In addition, there is the element of impulse, 
or change in momentum. Impulse is the product 
of force multiplied by change or interval in time. 
Again, the proportions of force and time interval 
do not matter, as long as they are equal to the 
momentum change — that is, the difference in 
momentum that occurs when the rifle is fired. To 
avoid injury to one’s shoulder, clearly force must 
be minimized, and for this to happen, time inter- 
val must be extended. 

If one were to fire the rifle with the stock 
(the rear end of the rifle) held at some distance 
from one’s shoulder, it would kick back and 
could very well produce a serious injury. This is 
because the force was delivered over a very short 
time interval — in other words, force was maxi- 
mized and time interval minimized. However, if 
one holds the rifle stock firmly against one’s 
shoulder, this slows down the delivery of the 
kick, thus maximizing time interval and mini- 
mizing force. 

rocketing through space. 

Contrary to popular belief, rockets do not move 
by pushing against a surface such as a launchpad. 
If that were the case, then a rocket would have 
nothing to propel it once it had been launched, 
and certainly there would be no way for a rocket 
to move through the vacuum of outer space. 
Instead, what propels a rocket is the conservation 
of momentum. 

Upon ignition, the rocket sends exhaust 
gases shooting downward at a high rate of veloc- 
ity. The gases themselves have mass, and thus, 
they have momentum. To balance this downward 
momentum, the rocket moves upward — though, 
because its mass is greater than that of the gases 
it expels, it will not move at a velocity as high as 
that of the gases. Once again, the upward or for- 
ward momentum is exactly the same as the 
downward or backward momentum, and linear 
momentum is conserved. 

Rather than needing something to push 
against, a rocket in fact performs best in outer 
space, where there is nothing — neither launch- 
pad nor even air — against which to push. Not 
only is “pushing” irrelevant to the operation of 


Conservation 

Laws 


SCIENCE GF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


3 1 


Conservation 

Laws 


KEY TERMS 


CONSERVATION LAWS: A Set of 

principles describing physical properties 
that remain constant — that is, are con- 
served — throughout the various processes 
that occur in the physical world. The most 
significant of these laws concerns the con- 
servation of energy (as well as, with quali- 
fications, the conservation of mass); con- 
servation of linear momentum; conserva- 
tion of angular momentum; and conserva- 
tion of electrical charge. 

CONSERVATION □ F ANGULAR MO- 
MENTUM: A physical law stating that 

when the sum of the external torques act- 
ing on a physical system is equal to zero, 
the total angular momentum of the system 
remains unchanged. Angular momentum 
is the momentum of an object in rotation- 
al motion, and torque is a force applied 
around an axis of rotation. 

CONSERVATION OF ELECTRICAL 

charge: A physical law which holds 

that for an isolated system, the net electri- 
cal charge is constant. 

CONSERVATION OF ENERGY: A 

law of physics stating that within a system 
isolated from all other outside factors, the 
total amount of energy remains the same, 
though transformations of energy from 
one form to another take place. 

CONSERVATION OF LINEAR MO- 
MENTUM: A physical law stating that 

when the sum of the external force vectors 
acting on a physical system is equal to zero, 
the total linear momentum of the system 
remains unchanged — or is conserved. 


conservation OF mass: A phys- 

ical principle stating that total mass is con- 
stant, and is unaffected by factors such as 
position, velocity, or temperature, in any 
system that does not exchange any matter 
with its environment. Unlike the other 
conservation laws, however, conservation 
of mass is not universally applicable, but 
applies only at speeds significant lower 
than that of light — 186,000 mi (297,600 
km) per second. Close to the speed of light, 
mass begins converting to energy. 

conserve: In physics, “to conserve” 

something means “to result in no net loss 
of” that particular component. It is possi- 
ble that within a given system, the compo- 
nent may change form or position, but as 
long as the net value of the component 
remains the same, it has been conserved. 

friction: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

momentum: A property that a mov- 

ing body possesses by virtue of its mass and 
velocity, which determines the amount of 
force and time required to stop it. 

system: In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 
all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 


32 


VDLUME 2: real-life physics 


SCIENCE OF EVERYDAY THINGS 



the rocket, but the rocket moves much more effi- 
ciently without the presence of air resistance. In 
the same way, on the relatively frictionless surface 
of an ice-skating rink, conservation of linear 
momentum (and hence, the process that makes 
possible the flight of a rocket through space) is 
easy to demonstrate. 

If, while standing on the ice, one throws an 
object in one direction, one will be pushed in the 
opposite direction with a corresponding level of 
momentum. However, since a person’s mass is 
presumably greater than that of the object 
thrown, the rearward velocity (and, therefore, 
distance) will be smaller. 

Friction, as noted earlier, is not the only 
force that counters conservation of linear 
momentum on Earth: so too does gravity, and 
thus, once again, a rocket operates much better in 
space than it does when under the influence of 
Earth’s gravitational field. If a bullet is fired at a 
bottle thrown into the air, the linear momentum 
of the spent bullet and the shattered pieces of 
glass in the infinitesimal moment just after the 
collision will be the same as that of the bullet and 
the bottle a moment before impact. An instant 
later, however, gravity will accelerate the bullet 
and the pieces downward, thus leading to a 
change in total momentum. 

Conservation of Angular 
Momentum: Skaters and 
□ ther Spinners 

As noted earlier, angular momentum is equal to 
mr 2 CG, where m is mass, r is the radius of rotation, 
and co stands for angular velocity. In fact, the first 
two quantities, mr 2 , are together known as 
moment of inertia. For an object in rotation, 
moment of inertia is the property whereby 
objects further from the axis of rotation move 
faster, and thus, contribute a greater share to the 
overall kinetic energy of the body. 

One of the most oft-cited examples of angu- 
lar momentum — and of its conservation — 
involves a skater or ballet dancer executing a 
spin. As the skater begins the spin, she has one leg 
planted on the ice, with the other stretched 
behind her. Likewise, her arms are outstretched, 
thus creating a large moment of inertia. But 
when she goes into the spin, she draws in her 


arms and leg, reducing the moment of inertia. In 
accordance with conservation of angular 
momentum, mr 2 CG will remain constant, and 
therefore, her angular velocity will increase, 
meaning that she will spin much faster. 

CONSTANT ORIENTATION. The 

motion of a spinning top and a Frisbee in flight 
also illustrate the conservation of angular 
momentum. Particularly interesting is the ten- 
dency of such an object to maintain a constant 
orientation. Thus, a top remains perfectly vertical 
while it spins, and only loses its orientation once 
friction from the floor dissipates its velocity and 
brings it to a stop. On a frictionless surface, how- 
ever, it would remain spinning — and therefore 
upright — forever. 

A Frisbee thrown without spin does not pro- 
vide much entertainment; it will simply fall to 
the ground like any other object. But if it is tossed 
with the proper spin, delivered from the wrist, 
conservation of angular momentum will keep it 
in a horizontal position as it flies through the air. 
Once again, the Frisbee will eventually be 
brought to ground by the forces of air resistance 
and gravity, but a Frisbee hurled through empty 
space would keep spinning for eternity. 

WHERE T □ LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Conservation Laws: An Online Physics Textbook” (Web 
site). 

<http://www.lightandmatter.com/arealbook2.html> 
(March 12, 2001). 

“Conservation Laws: The Most Powerful Laws of Physics” 
(Web site). 

<http://webug.physics.uiuc.edu/courses/physl50/fall 
99/slides/lectO 7 /> (March 12, 2001). 

“Conservation of Energy.” NASA (Web site). 
<http://www.grc.nasa.gov/WWW/K- 
12/airplane/thermolf.html> (March 12, 2001). 

Elkana, Yehuda. The Discovery of the Conservation of 
Energy. With a foreword by I. Bernard Cohen. Cam- 
bridge, MA: Harvard University Press, 1974. 

“Momentum and Its Conservation” (Web site). 

<http://www.glenbrook.kl2.il.us/gbssci/phys/Class/ 
momentum/momtoc. html> (March 12, 2001). 

Rutherford, E James; Gerald Holton; and Fletcher G. 
Watson. Project Physics. New York: Holt, Rinehart, 
and Winston, 1981. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 


Conservation 

Laws 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


33 


SCIENCE DF EVERYDAY THINGS 

REAL-LIFE PHYSICS 

K I N E M AT ICS AND 
PARTICLE DYNAMICS 

MOMENTUM 
CENTRIPETAL FORCE 
FRICTION 
LAWS OF MOTION 
G R A V I T Y 
PROJECTILE MOTION 
TORQUE 


35 



MOMENTUM 


C □ N C E PT 

The faster an object is moving — whether it be a 
baseball, an automobile, or a particle of matter — 
the harder it is to stop. This is a reflection of 
momentum, or specifically, linear momentum, 
which is equal to mass multiplied by velocity. 
Like other aspects of matter and motion, 
momentum is conserved, meaning that when the 
vector sum of outside forces equals zero, no net 
linear momentum within a system is ever lost or 
gained. A third important concept is impulse, the 
product of force multiplied by length in time. 
Impulse, also defined as a change in momentum, 
is reflected in the proper methods for hitting a 
baseball with force or surviving a car crash. 

H □ W IT WDRKS 

Like many other aspects of physics, the word 
“momentum” is a part of everyday life. The com- 
mon meaning of momentum, however, unlike 
many other physics terms, is relatively consistent 
with its scientific meaning. In terms of formula, 
momentum is equal to the product of mass and 
velocity, and the greater the value of that prod- 
uct, the greater the momentum. 

Consider the term “momentum” outside the 
world of physics, as applied, for example, in the 
realm of politics. If a presidential candidate sees 
a gain in public-opinion polls, then wins a debate 
and embarks on a whirlwind speaking tour, the 
media comments that he has “gained momen- 
tum.” As with momentum in the framework of 
physics, what these commentators mean is that 
the candidate will be hard to stop — or to carry 
the analogy further, that he is doing enough of 
the right things (thus gaining “mass”), and doing 
them quickly enough, thereby gaining velocity. 

SCIENCE □ E EVERYDAY THINGS 


Momentum and Inertia 

It might be tempting to confuse momentum with 
another physical concept, inertia. Inertia, as 
defined by the second law of motion, is the ten- 
dency of an object in motion to remain in 
motion, and of an object at rest to remain at rest. 
Momentum, by definition, involves a body in 
motion, and can be defined as the tendency of a 
body in motion to continue moving at a constant 
velocity. 

Not only does momentum differ from iner- 
tia in that it relates exclusively to objects in 
motion, but (as will be discussed below) the 
component of velocity in the formula for 
momentum makes it a vector — that is, a quanti- 
ty that possesses both magnitude and direction. 
There is at least one factor that momentum very 
clearly has in common with inertia: mass, a 
measure of inertia indicating the resistance of an 
object to a change in its motion. 

Mass and Weight 

Unlike velocity, mass is a scalar, a quantity that 
possesses magnitude without direction. Mass is 
often confused with weight, a vector quantity 
equal to its mass multiplied by the downward 
acceleration due to gravity. The weight of an 
object changes according to the gravitational 
force of the planet or other celestial body on 
which it is measured. Hence, the mass of a person 
on the Moon would be the same as it is on Earth, 
whereas the person’s weight would be consider- 
ably less, due to the smaller gravitational pull of 
the Moon. 

Given the unchanging quality of mass as 
opposed to weight, as well as the fact that scien- 
tists themselves prefer the much simpler metric 

VDLUME 2: REAL-LIFE PHYSICS 


37 



Momentum 



When billiard balls collide, their hardness results in an elastic collision — one in which kinetic ener- 
gy is conserved. (Photograph by John-Marshall Mantel/Corbis. Reproduced by permission.) 


3B 


system, metric units will generally be used in the 
following discussion. Where warranted, of 
course, conversion to English or British units (for 
example, the pound, a unit of weight) will be 
provided. However, since the English unit of 
mass, the slug, is even more unfamiliar to most 
Americans than its metric equivalent, the kilo- 
gram, there is little point in converting kilos into 
slugs. 

Velocity and Speed 

Not only is momentum often confused with 
inertia, and mass with weight, but in the everyday 
world the concepts of velocity and speed tend to 
be blurred. Speed is the rate at which the position 
of an object changes over a given period of time, 
expressed in terms such as “50 MPH.” It is a 
scalar quantity. 

Velocity, by contrast, is a vector. If one were 
to say “50 miles per hour toward the northeast,” 
this would be an expression of velocity. Vectors 
are typically designated in bold, without italics; 
thus velocity is typically abbreviated v. Scalars, 
on the other hand, are rendered in italics. Hence, 
the formula for momentum is usually shown 
as mv. 

VDLUME 2: REAL-LIFE PHYSICS 


Linear Momentum and Its 
Conservation 

Momentum itself is sometimes designated as p. It 
should be stressed that the form of momentum 
discussed here is strictly linear, or straight-line, 
momentum, in contrast to angular momentum, 
more properly discussed within the framework 
of rotational motion. 

Both angular and linear momentum abide 
by what are known as conservation laws. These 
are statements concerning quantities that, under 
certain conditions, remain constant or unchang- 
ing. The conservation of linear momentum law 
states that when the sum of the external force 
vectors acting on a physical system is equal to 
zero, the total linear momentum of the system 
remains unchanged — or conserved. 

The conservation of linear momentum is 
reflected both in the recoil of a rifle and in the 
propulsion of a rocket through space. When a 
rifle is fired, it produces a “kick” — that is, a sharp 
jolt to the shoulder of the person who has fired 
it — corresponding to the momentum of the bul- 
let. Why, then, does the “kick” not knock a per- 
son’s shoulder off the way a bullet would? Because 
the rifle’s mass is much greater than that of the 
bullet, meaning that its velocity is much smaller. 

SCIENCE OF EVERYDAY THINGS 


As for rockets, they do not — contrary to 
popular belief — move by pushing against a sur- 
face, such as a launch pad. If that were the case, 
then a rocket would have nothing to propel it 
once it is launched, and certainly there would be 
no way for a rocket to move through the vacuum 
of outer space. Instead, as it burns fuel, the rock- 
et expels exhaust gases that exert a backward 
momentum, and the rocket itself travels forward 
with a corresponding degree of momentum. 

Systems 

Here, “system” refers to any set of physical inter- 
actions isolated from the rest of the universe. 
Anything outside of the system, including all fac- 
tors and forces irrelevant to a discussion of that 
system, is known as the environment. In the 
pool-table illustration shown earlier, the interac- 
tion of the billiard balls in terms of momentum 
is the system under discussion. 

It is possible to reduce a system even further 
for purposes of clarity: hence, one might specify 
that the system consists only of the pool balls, the 
force applied to them, and the resulting momen- 
tum interactions. Thus, we will ignore the fric- 
tion of the pool table’s surface, and the assump- 
tion will be that the balls are rolling across a fric- 
tionless plane. 

Impulse 

For an object to have momentum, some force 
must have set it in motion, and that force must 
have been applied over a period of time. Like- 
wise, when the object experiences a collision or 
any other event that changes its momentum, that 
change may be described in terms of a certain 
amount of force applied over a certain period of 
time. Force multiplied by time interval is 
impulse, expressed in the formula F • 8 1 , where F 
is force, 8 (the Greek letter delta) means “a 
change” or “change in...”; and t is time. 

As with momentum itself, impulse is a vec- 
tor quantity. Whereas the vector component of 
momentum is velocity, the vector quantity in 
impulse is force. The force component of 
impulse can be used to derive the relationship 
between impulse and change in momentum. 
According to the second law of motion, F = m a; 
that is, force is equal to mass multiplied by accel- 
eration. Acceleration can be defined as a change 

SCIENCE □ E EVERYDAY THINGS 



When parachutists land, they keep their knees 

BENT AND OFTEN ROLL OVER ALL IN AN EFFORT TO 

LENGTHEN THE PERIOD OF THE FORCE OF IMPACT, THUS 

reducing its effects. (Photograph by James A. Sugar/Corbis. 
Reproduced by permission.) 

in velocity over a change or interval in time. 
Expressed as a formula, this is 


Thus, force is equal to 



an equation that can be rewritten as F8f = m 8v. 
In other words, impulse is equal to change in 
momentum. 

This relationship between impulse and 
momentum change, derived here in mathematical 
terms, will be discussed below in light of several 
well-known examples from the real world. Note 
that the metric units of impulse and momentum 
are actually interchangeable, though they are typ- 
ically expressed in different forms, for the purpose 
of convenience. Hence, momentum is usually ren- 
dered in terms of kilogram-meters-per-second 
(kg • m/s), whereas impulse is typically shown as 
newton-seconds (N • s). In the English system, 
momentum is shown in units of slug-feet per- 

VDLUME 2: REAL-LIFE PHYSICS 


Momentum 


39 



Momentum 


4 □ 



As Sammy Sosa’s bat hits this ball, it applies a 

TREMENDOUS MOMENTUM CHANGE TO THE BALL. AFTER 
CONTACT WITH THE BALL, SOSA WILL CONTINUE HIS 
SWING, THEREBY CONTRIBUTING TO THE MOMENTUM 
CHANGE AND ALLOWING THE BALL TO TRAVEL FARTHER. 

(AFP/Corbis. Reproduced by permission.) 

second, and impulse in terms of the pound- 
second. 

REAL-LIFE 
A P P L I C AT I □ N S 

When Two Objects Collide 

Two moving objects, both possessing momen- 
tum by virtue of their mass and velocity, collide 
with one another. Within the system created by 
their collision, there is a total momentum MV 
that is equal to their combined mass and the vec- 
tor sum of their velocity. 

This is the case with any system: the total 
momentum is the sum of the various individual 
momentum products. In terms of a formula, this 
is expressed as MV = m l \ 1 + m 2 v 2 + m 3 v 3 +... and 
so on. As noted earlier, the total momentum will 
be conserved; however, the actual distribution of 
momentum within the system may change. 

two lumps df clay. Consider 
the behavior of two lumps of clay, thrown at one 

VDLUME 2: REAL-LIFE PHYSICS 


another so that they collide head-on. Due to the 
properties of clay as a substance, the two lumps 
will tend to stick. Assuming the lumps are not 
of equal mass, they will continue traveling in 
the same direction as the lump with greater 
momentum. 

As they meet, the two lumps form a larger 
mass MV that is equal to the sum of their two 
individual masses. Once again, MV = m l v l + 
m 2 x 2 . The M in MV is the sum of the smaller val- 
ues m, and the V is the vector sum of velocity. 
Whereas M is larger than m 1 or m 2 — the reason 
being that scalars are simply added like ordinary 
numbers — V is smaller than or v 2 . This lower 

number for net velocity as compared to particle 
velocity will always occur when two objects are 
moving in opposite directions. (If the objects are 
moving in the same direction, V will have a value 
between that of v t and v 2 .) 

To add the vector sum of the two lumps in 
collision, it is best to make a diagram showing the 
bodies moving toward one another, with arrows 
illustrating the direction of velocity. By conven- 
tion, in such diagrams the velocity of an object 
moving to the right is rendered as a positive 
number, and that of an object moving to the left 
is shown with a negative number. It is therefore 
easier to interpret the results if the object with 
the larger momentum is shown moving to the 
right. 

The value of V will move in the same direc- 
tion as the lump with greater momentum. But 
since the two lumps are moving in opposite 
directions, the momentum of the smaller lump 
will cancel out a portion of the greater lump’s 
momentum — much as a negative number, when 
added to a positive number of greater magni- 
tude, cancels out part of the positive number’s 
value. They will continue traveling in the direc- 
tion of the lump with greater momentum, now 
with a combined mass equal to the arithmetic 
sum of their masses, but with a velocity much 
smaller than either had before impact. 

billiard balls. The game of pool 
provides an example of a collision in which one 
object, the cue ball, is moving, while the other — 
known as the object ball — is stationary. Due to 
the hardness of pool balls, and their tendency not 
to stick to one another, this is also an example of 
an almost perfectly elastic collision — one in 
which kinetic energy is conserved. 

SCIENCE DF EVERYDAY THINGS 


Momentum 


The colliding lumps of clay, on the other 
hand, are an excellent example of an inelastic col- 
lision, or one in which kinetic energy is not con- 
served. The total energy in a given system, such as 
that created by the two lumps of clay in collision, 
is conserved; however, kinetic energy may be 
transformed, for instance, into heat energy 
and/or sound energy as a result of collision. 
Whereas inelastic collisions involve soft, sticky 
objects, elastic collisions involve rigid, non-sticky 
objects. 

Kinetic energy and momentum both involve 
components of velocity and mass: p (momen- 
tum) is equal to mv, and KE (kinetic energy) 
equals / mv 2 . Due to the elastic nature of pool- 
ball collisions, when the cue ball strikes the 
object ball, it transfers its velocity to the latter. 
Their masses are the same, and therefore the 
resulting momentum and kinetic energy of the 
object ball will be the same as that possessed by 
the cue ball prior to impact. 

If the cue ball has transferred all of its veloc- 
ity to the object ball, does that mean it has 
stopped moving? It does. Assuming that the 
interaction between the cue ball and the object 
ball constitutes a closed system, there is no other 
source from which the cue ball can acquire veloc- 
ity, so its velocity must be zero. 

It should be noted that this illustration treats 
pool-ball collisions as though they were 100% 
elastic, though in fact, a portion of kinetic ener- 
gy in these collisions is transformed into heat and 
sound. Also, for a cue ball to transfer all of its 
velocity to the object ball, it must hit it straight- 
on. If the balls hit off-center, not only will the 
object ball move after impact, but the cue ball 
will continue to move — roughly at 90° to a line 
drawn through the centers of the two balls at the 
moment of impact. 

Impulse: Breaking or Build- 
ing the Impact 

When a cue ball hits an object ball in pool, it is 
safe to assume that a powerful impact is desired. 
The same is true of a bat hitting a baseball. But 
what about situations in which a powerful 
impact is not desired — as for instance when cars 
are crashing? There is, in fact, a relationship 
between impulse, momentum change, transfer of 
kinetic energy, and the impact — desirable or 
undesirable — experienced as a result. 

SCIENCE □ E EVERYDAY THINGS 


Impulse, again, is equal to momentum 
change — and also equal to force multiplied by 
time interval (or change in time). This means 
that the greater the force and the greater the 
amount of time over which it is applied, the 
greater the momentum change. Even more inter- 
esting is the fact that one can achieve the same 
momentum change with differing levels of force 
and time interval. In other words, a relatively low 
degree of force applied over a relatively long peri- 
od of time would produce the same momentum 
change as a relatively high amount of force over a 
relatively short period of time. 

The conservation of kinetic energy in a col- 
lision is, as noted earlier, a function of the relative 
elasticity of that collision. The question of 
whether KE is transferred has nothing to do with 
impulse. On the other hand, the question of how 
KE is transferred — or, even more specifically, the 
interval over which the transfer takes place — is 
very much related to impulse. 

Kinetic energy, again, is equal to 'A mv 2 . If a 
moving car were to hit a stationary car head-on, 
it would transfer a quantity of kinetic energy to 
the stationary car equal to one-half its own 
mass multiplied by the square of its velocity. 
(This, of course, assumes that the collision is 
perfectly elastic, and that the mass of the cars is 
exactly equal.) A transfer of KE would also 
occur if two moving cars hit one another head- 
on, especially in a highly elastic collision. 
Assuming one car had considerably greater 
mass and velocity than the other, a high degree 
of kinetic energy would be transferred — which 
could have deadly consequences for the people 
in the car with less mass and velocity. Even with 
cars of equal mass, however, a high rate of accel- 
eration can bring about a potentially lethal 
degree of force. 

CRUMPLE ZDNES IN CARS. In 

a highly elastic car crash, two automobiles would 
bounce or rebound off one another. This would 
mean a dramatic change in direction — a reversal, 
in fact — hence, a sudden change in velocity and 
therefore momentum. In other words, the figure 
for m8v would be high, and so would that for 
impulse, F8t. 

On the other hand, it is possible to have a 
highly inelastic car crash, accompanied by a 
small change in momentum. It may seem logical 
to think that, in a crash situation, it would be bet- 
ter for two cars to bounce off one another than 

VDLUME 2: REAL-LIFE PHYSICS 


4 1 


Momentum 


KEY TERMS 


acceleration: A change velocity. 

Acceleration can be expressed as a formula 
8v/8t — that is, change in velocity divided 
by change, or interval, in time. 

CONSERVATION DF LINEAR 

momentum: A physical law, which 

states that when the sum of the external 
force vectors acting on a physical system is 
equal to zero, the total linear momentum 
of the system remains unchanged — or is 
conserved. 

conserve: In physics, “to conserve” 

something (for example, momentum or 
kinetic energy) means “to result in no net 
loss of” that particular component. It is 
possible that within a given system, one 
type of energy may be transformed into 
another type, but the net energy in the sys- 
tem will remain the same. 

elastic collision: A collision in 

which kinetic energy is conserved. Typical- 
ly elastic collisions involve rigid, non-sticky 
objects such as pool balls. At the other 
extreme is an inelastic collision. 


impulse: The amount of force and 

time required to cause a change in 
momentum. Impulse is the product of 
force multiplied by a change, or interval, in 
time (FSt): the greater the momentum, 

the greater the force needed to change it, 
and the longer the period of time over 
which it must be applied. 

inelastic collision: A collision 

in which kinetic energy is not conserved. 
(The total energy is conserved: kinetic 
energy itself, however, may be transformed 
into heat energy or sound energy.) Typical- 
ly, inelastic collisions involve non-rigid, 
sticky objects — for instance, lumps of clay. 
At the other extreme is an elastic collision. 

i n e rti a: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

kinetic energy: The energy an 

object possesses by virtue of its motion. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 


42 


for them to crumple together. In fact, however, 
the latter option is preferable. When the cars 
crumple rather than rebounding, they do not 
experience a reversal in direction. They do expe- 
rience a change in speed, of course, but the 
momentum change is far less than it would be if 
they rebounded. 

Furthermore, crumpling lengthens the 
amount of time during which the change in 
velocity occurs, and thus reduces impulse. But 
even with the reduced impulse of this momen- 
tum change, it is possible to further reduce the 
effect of force, another aspect of impact. Remem- 
ber that «z8v = F8f: the value of force and time 
interval do not matter, as long as their product is 
equal to the momentum change. Because F and 

vdlume z: real-life physics 


8f are inversely proportional, an increase in 
impact time will reduce the effects of force. 

For this reason, car manufacturers actually 
design and build into their cars a feature known 
as a crumple zone. A crumple zone — and there 
are usually several in a single automobile — is a 
section in which the materials are put together in 
such a way as to ensure that they will crumple 
when the car experiences a collision. Of course, 
the entire car cannot be one big crumple zone — 
this would be fatal for the driver and riders; how- 
ever, the incorporation of crumple zones at key 
points can greatly reduce the effect of the force a 
car and its occupants must endure in a crash. 

Another major reason for crumple zones is 
to keep the passenger compartment of the car 

SCIENCE GF EVERYDAY THINGS 



Momentum 


KEY TERMS continued 


motion — including a change in velocity. A 
kilogram is a unit of mass, whereas a 
pound is a unit of weight. 

momentum: A property that a mov- 

ing body possesses by virtue of its mass and 
velocity, which determines the amount of 
force and time (impulse) required to stop 
it. Momentum — actually linear momen- 
tum, as opposed to the angular momen- 
tum of an object in rotational motion — is 
equal to mass multiplied by velocity. 

scalar: A quantity that possesses 

only magnitude, with no specific direc- 
tion — as contrasted with a vector, which 
possesses both magnitude and direction. 
Scalar quantities are usually expressed in 
italicized letters, thus: m (mass). 

speed: The rate at which the position 

of an object changes over a given period of 
time. 

syste m : In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 


all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 

vector: A quantity that possesses 

both magnitude and direction — as con- 
trasted with a scalar, which possesses mag- 
nitude without direction. Vector quantities 
are usually expressed in bold, non-itali- 
cized letters, thus: F (force). They may also 
be shown by placing an arrow over the let- 
ter designating the specific property, as for 
instance v for velocity. 

vector sum: A calculation that 

yields the net result of all the vectors 
applied in a particular situation. In the case 
of momentum, the vector component is 
velocity. The best method is to make a dia- 
gram showing bodies in collision, with 
arrows illustrating the direction of velocity. 
On such a diagram, motion to the right is 
assigned a positive value, and to the left a 
negative value. 

veldc ity: The speed of an object in a 

particular direction. 


intact. Many injuries are caused when the body 
of the car intrudes on the space of the occu- 
pants — as, for instance, when the floor buckles, 
or when the dashboard is pushed deep into the 
passenger compartment. Obviously, it is pre- 
ferable to avoid this by allowing the fender to 
collapse. 

REDUCING IMPULSE: SAVING 

LIVES, BONES, AND WATER BAL- 
LOONS. An airbag is another way of mini- 
mizing force in a car accident, in this case by 
reducing the time over which the occupants 
move forward toward the dashboard or wind- 
shield. The airbag rapidly inflates, and just as 
rapidly begins to deflate, within the split-second 
that separates the car’s collision and a person’s 

SCIENCE OF EVERYDAY THINGS 


collision with part of the car. As it deflates, it is 
receding toward the dashboard even as the dri- 
ver’s or passenger’s body is being hurled toward 
the dashboard. It slows down impact, extending 
the amount of time during which the force is dis- 
tributed. 

By the same token, a skydiver or paratroop- 
er does not hit the ground with legs outstretched: 
he or she would be likely to suffer a broken bone 
or worse from such a foolish stunt. Rather, as a 
parachutist prepares to land, he or she keeps 
knees bent, and upon impact immediately rolls 
over to the side. Thus, instead of experiencing the 
force of impact over a short period of time, the 
parachutist lengthens the amount of time that 
force is experienced, which reduces its effects. 

VOLUME 2: REAL-LIFE PHYSICS 


43 



Momentum 


The same principle applies if one were 
catching a water balloon. In order to keep it from 
bursting, one needs to catch the balloon in 
midair, then bring it to a stop slowly by “travel- 
ing” with it for a few feet before reducing its 
momentum down to zero. Once again, there is 
no way around the fact that one is attempting to 
bring about a substantial momentum change — a 
change equal in value to the momentum of the 
object in movement. Nonetheless, by increasing 
the time component of impulse, one reduces the 
effects of force. 

In old Superman comics, the “Man of Steel” 
often caught unfortunate people who had fallen, 
or been pushed, out of tall buildings. The car- 
toons usually showed him, at a stationary posi- 
tion in midair, catching the person before he or 
she could hit the ground. In fact, this would not 
save their lives: the force component of the sud- 
den momentum change involved in being caught 
would be enough to kill the person. Of course, it 
is a bit absurd to quibble over scientific accuracy 
in Superman, but in order to make the situation 
more plausible, the “Man of Steel” should have 
been shown catching the person, then slowly fol- 
lowing through on the trajectory of the fall 
toward earth. 

THE CRACK OF THE BAT: 
INCREASING IMPULSE. But what if — 

to once again turn the tables — a strong force is 
desired? This time, rather than two pool balls 
striking one another, consider what happens 
when a batter hits a baseball. Once more, the cor- 
relation between momentum change and impulse 
can create an advantage, if used properly. 

As the pitcher hurls the ball toward home 
plate, it has a certain momentum; indeed, a pitch 
thrown by a major-league player can send the 
ball toward the batter at speeds around 100 MPH 
(160 km/h) — a ball having considerable momen- 
tum). In order to hit a line drive or “knock the 
ball out of the park,” the batter must therefore 
cause a significant change in momentum. 

Consider the momentum change in terms of 
the impulse components. The batter can only 
apply so much force, but it is possible to magnify 
impulse greatly by increasing the amount of time 
over which the force is delivered. This is known in 


sports — and it applies as much in tennis or golf as 
in baseball — as “following through.” By increas- 
ing the time of impact, the batter has increased 
impulse and thus, momentum change. Obvious- 
ly, the mass of the ball has not been altered; the 
difference, then, is a change in velocity. 

How is it possible that in earlier examples, 
the effects of force were decreased by increasing 
the time interval, whereas in the baseball illustra- 
tion, an increase in time interval resulted in a 
more powerful impact? The answer relates to dif- 
ferences in direction and elasticity. The baseball 
and the bat are colliding head-on in a relatively 
elastic situation; by contrast, crumpling cars are 
inelastic. In the example of a person catching a 
water balloon, the catcher is moving in the same 
direction as the balloon, thus reducing momen- 
tum change. Even in the case of the paratrooper, 
the ground is stationary; it does not move toward 
the parachutist in the way that the baseball 
moves toward the bat. 

WHERE TD LEARN MDRE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Bonnet, Robert L. and Dan Keen. Science Fair Projects: 
Physics. Illustrated by Frances Zweifel. New York: 
Sterling, 1999. 

Fleisher, Paul. Objects in Motion: Principles of Classical 
Mechanics. Minneapolis, MN: Lerner Publications, 
2002 . 

Gardner, Robert. Experimenting with Science in Sports. 
New York: F. Watts, 1993. 

“Lesson 1: The Impulse Momentum Change Theorem” 
(Web site) 

<http://www.glenbrook.kl2.il.us/gbssci/phys/Class/ 
momentum/u411a.html> (March 19, 2001). 

“Momentum” (Web site). 

<http://id.mind.net/~zona/mstm/physics/mechan- 
ics/momentum/momentum.html> (March 19, 2001). 

Physlink.com (Web site), <http://www.physlink.com> 
(March 7, 2001). 

Rutherford, F. James; Gerald Flolton; and Fletcher G. 
Watson. Project Physics. New York: Flolt, Rinehart, 
and Winston, 1981. 

Schrier, Eric and William F. Allman. Newton at the Bat: 
The Science in Sports. New York: Charles Scribner’s 
Sons, 1984. 

Zubrowski, Bernie. Raceways: Having Fun with Balls and 
Tracks. Illustrated by Roy Doty. New York: William 
Morrow, 1985. 


44 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


CENTRIPETAL FORCE 


C □ N C E PT 

Most people have heard of centripetal and cen- 
trifugal force. Though it may be somewhat diffi- 
cult to keep track of which is which, chances are 
anyone who has heard of the two concepts 
remembers that one is the tendency of objects in 
rotation to move inward, and the other is the ten- 
dency of rotating objects to move outward. It 
may come as a surprise, then, to learn that there 
is no such thing, strictly speaking, as centrifugal 
(outward) force. There is only centripetal 
(inward) force and the inertia that makes objects 
in rotation under certain situations move out- 
ward, for example, a car making a turn, the 
movement of a roller coaster — even the spinning 
of a centrifuge. 

H □ W IT WDRKS 

Like many other principles in physics, centripetal 
force ultimately goes back to a few simple pre- 
cepts relating to the basics of motion. Consider 
an object in uniform circular motion: an object 
moves around the center of a circle so that its 
speed is constant or unchanging. 

The formula for speed — or rather, average 
speed — is distance divided by time; hence, peo- 
ple say, for instance, “miles (or kilometers) per 
hour.” In the case of an object making a circle, 
distance is equal to the circumference, or dis- 
tance around, the circle. From geometry, we 
know that the formula for calculating the cir- 
cumference of a circle is 2nr, where r is the 
radius, or the distance from the circumference to 
the center. The figure n may be rendered as 
3.141592..., though in fact, it is an irrational 
number: the decimal figures continue forever 
without repetition or pattern. 

SCIENCE □ F EVERYDAY THINGS 


From the above, it can be discerned that the 
formula for the average speed of an object moving 
around a circle is 2nr divided by time. Further- 
more, we can see that there is a proportional rela- 
tionship between radius and average speed. If the 
radius of a circle is doubled, but an object at the 
circle’s periphery makes one complete revolution 
in the same amount of time as before, this means 
that the average speed has doubled as well. This 
can be shown by setting up two circles, one with a 
radius of 2, the other with a radius of 4, and using 
some arbitrary period of time — say, 2 seconds. 

The above conclusion carries with it an 
interesting implication with regard to speeds at 
different points along the radius of a circle. 
Rather than comparing two points moving 
around the circumferences of two different cir- 
cles — one twice as big as the other — in the same 
period of time, these two points could be on the 
same circle: one at the periphery, and one exact- 
ly halfway along the radius. Assuming they both 
traveled a complete circle in the same period of 
time, the proportional relationship described 
earlier would apply. This means, then, that the 
further out on the circle one goes, the greater the 
average speed. 

Velocity = Speed + Direction 

Speed is a scalar, meaning that it has magnitude 
but no specific direction; by contrast, velocity is a 
vector — a quantity with both a magnitude (that 
is, speed) and a direction. For an object in circu- 
lar motion, the direction of velocity is the same 
as that in which the object is moving at any given 
point. Consider the example of the city of 
Atlanta, Georgia, and Interstate-285, one of sev- 
eral instances in which a city is surrounded by a 
“loop” highway. Local traffic reporters avoid giv- 

VDLUME 2: REAL-LIFE PHYSICS 


45 



Centripetal 

Force 



Typically, a centrifuge consists of a base; a 

ROTATING TUBE PERPENDICULAR TO THE BASE; AND 
VIALS ATTACHED BY MOVABLE CENTRIFUGE ARMS TO THE 
ROTATING TUBE. THE MOVABLE ARMS ARE HINGED AT 
THE TOP OF THE ROTATING TUBE, AND THUS CAN MOVE 
UPWARD AT AN ANGLE APPROACHING 9D° TO THE TUBE. 

When the tube begins to spin, centripetal force 

PULLS THE MATERIAL IN THE VIALS TOWARD THE CEN- 
TER. (Photograph by Charles D. Winters. National Audubon Society 
Collection/Photo Researchers, Inc. Reproduced by permission.) 

ing mere directional coordinates for spots on that 
highway (for instance, “southbound on 285”), 
because the area where traffic moves south 
depends on whether one is moving clockwise or 
counterclockwise. Hence, reporters usually say 
“southbound on the outer loop.” 

As with cars on 1-285, the direction of the 
velocity vector for an object moving around a 
circle is a function entirely of its position and the 
direction of movement — clockwise or counter- 
clockwise — for the circle itself. The direction of 
the individual velocity vector at any given point 
may be described as tangential; that is, describing 
a tangent, or a line that touches the circle at just 
one point. (By definition, a tangent line cannot 
intersect the circle.) 

It follows, then, that the direction of an object 
in movement around a circle is changing; hence, 
its velocity is also changing — and this in turn 


means that it is experiencing acceleration. As with 
the subject of centripetal force and “centrifugal 
force,” most people have a mistaken view of accel- 
eration, believing that it refers only to an increase 
in speed. In fact, acceleration is a change in veloc- 
ity, and can thus refer either to a change in speed 
or direction. Nor must that change be a positive 
one; in other words, an object undergoing a reduc- 
tion in speed is also experiencing acceleration. 

The acceleration of an object in rotational 
motion is always toward the center of the circle. 
This may appear to go against common sense, 
which should indicate that acceleration moves in 
the same direction as velocity, but it can, in fact, 
be proven in a number of ways. One method 
would be by the addition of vectors, but a 
“hands-on” demonstration may be more enlight- 
ening than an abstract geometrical proof. 

It is possible to make a simple accelerometer, 
a device for measuring acceleration, with a lit can- 
dle inside a glass. The candle should be standing 
at a 90°-angle to the bottom of the glass, attached 
to it by hot wax as you would affix a burning can- 
dle to a plate. When you hold the candle level, the 
flame points upward; but if you spin the glass in a 
circle, the flame will point toward the center of 
that circle — in the direction of acceleration. 

Mass X Acceleration = Force 

Since we have shown that acceleration exists for 
an object spinning around a circle, it is then pos- 
sible for us to prove that the object experiences 
some type of force. The proof for this assertion 
lies in the second law of motion, which defines 
force as the product of mass and acceleration: 
hence, where there is acceleration and mass, there 
must be force. Force is always in the direction of 
acceleration, and therefore the force is directed 
toward the center of the circle. 

In the above paragraph, we assumed the 
existence of mass, since all along the discussion 
has concerned an object spinning around a circle. 
By definition, an object — that is, an item of mat- 
ter, rather than an imaginary point — possesses 
mass. Mass is a measure of inertia, which can be 
explained by the first law of motion: an object in 
motion tends to remain in motion, at the same 
speed and in the same direction (that is, at the 
same velocity) unless or until some outside force 
acts on it. This tendency to maintain velocity is 
inertia. Put another way, it is inertia that causes 
an object standing still to remain motionless, and 


46 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



A CLDTHDID LOOP IN A ROLLER COASTER IN HAINES ClTY, FLORIDA. At THE TOP OF A LOOP, YOU FEEL LIGHTER 

than normal; at th e bottom, you feel heavier. (The Purcell Team/Corbis. Reproduced by permission.) 


likewise, it is inertia which dictates that a moving 
object will “try” to keep moving. 

Centripetal Fdrce 

Now that we have established the existence of a 
force in rotational motion, it is possible to give it 
a name: centripetal force, or the force that causes 
an object in uniform circular motion to move 
toward the center of the circular path. This is not 
a “new” kind of force; it is merely force as applied 
in circular or rotational motion, and it is 
absolutely essential. Hence, physicists speak of a 
“centripetal force requirement”: in the absence of 
centripetal force, an object simply cannot turn. 
Instead, it will move in a straight line. 

The Latin roots of centripetal together mean 

SCIENCE □ E EVERYDAY THINGS 


“seeking the center.” What, then, of centrifugal, a 
word that means “fleeing the center”? It would be 
correct to say that there is such a thing as cen- 
trifugal motion; but centrifugal force is quite a 
different matter. The difference between cen- 
tripetal force and a mere centrifugal tendency — 
a result of inertia rather than of force — can be 
explained by referring to a familiar example. 

REAL-LIFE 
A P P L I C AT I D N S 

Riding in a Car 

When you are riding in a car and the car acceler- 
ates, your body tends to move backward against 

VDLUME 2: REAL-LIFE PHYSICS 


4V 


Centripetal 

Force 


the seat. Likewise, if the car stops suddenly, your 
body tends to move forward, in the direction of 
the dashboard. Note the language here: “tends to 
move” rather than “is pushed.” To say that some- 
thing is pushed would imply that a force has been 
applied, yet what is at work here is not a force, 
but inertia — the tendency of an object in motion 
to remain in motion, and an object at rest to 
remain at rest. 

A car that is not moving is, by definition, at 
rest, and so is the rider. Once the car begins mov- 
ing, thus experiencing a change in velocity, the 
rider’s body still tends to remain in the fixed posi- 
tion. Hence, it is not a force that has pushed the 
rider backward against the seat; rather, force has 
pushed the car forward, and the seat moves up to 
meet the rider’s back. When stopping, once again, 
there is a sudden change in velocity from a certain 
value down to zero. The rider, meanwhile, is con- 
tinuing to move forward due to inertia, and thus, 
his or her body has a tendency to keep moving in 
the direction of the now-stationary dashboard. 

This may seem a bit too simple to anyone 
who has studied inertia, but because the human 
mind has such a strong inclination to perceive 
inertia as a force in itself, it needs to be clarified 
in the most basic terms. This habit is similar to 
the experience you have when sitting in a vehicle 
that is standing still, while another vehicle along- 
side moves backward. In the first split-second of 
awareness, your mind tends to interpret the 
backward motion of the other car as forward 
motion on the part of the car in which you are 
sitting — even though your own car is standing 
still. 

Now we will consider the effects of cen- 
tripetal force, as well as the illusion of centrifugal 
force. When a car turns to the left, it is undergo- 
ing a form of rotation, describing a 90°-angle or 
one-quarter of a circle. Once again, your body 
experiences inertia, since it was in motion along 
with the car at the beginning of the turn, and 
thus you tend to move forward. The car, at the 
same time, has largely overcome its own inertia 
and moved into the leftward turn. Thus the car 
door itself is moving to the left. As the door 
meets the right side of your body, you have the 
sensation of being pushed outward against the 
door, but in fact what has happened is that the 
door has moved inward. 

The illusion of centrifugal force is so deeply 
ingrained in the popular imagination that it war- 


rants further discussion below. But while on the 
subject of riding in an automobile, we need to 
examine another illustration of centripetal force. 
It should be noted in this context that for a car to 
make a turn at all, there must be friction between 
the tires and the road. Friction is the force that 
resists motion when the surface of one object 
comes into contact with the surface of another; 
yet ironically, while opposing motion, friction 
also makes relative motion possible. 

Suppose, then, that a driver applies the 
brakes while making a turn. This now adds a 
force tangential, or at a right angle, to the cen- 
tripetal force. If this force is greater than the cen- 
tripetal force — that is, if the car is moving too 
fast — the vehicle will slide forward rather than 
making the turn. The results, as anyone who has 
ever been in this situation will attest, can be dis- 
astrous. 

The above highlights the significance of the 
centripetal force requirement: without a suffi- 
cient degree of centripetal force, an object simply 
cannot turn. Curves are usually banked to maxi- 
mize centripetal force, meaning that the roadway 
tilts inward in the direction of the curve. This 
banking causes a change in velocity, and hence, in 
acceleration, resulting in an additional quantity 
known as reaction force, which provides the 
vehicle with the centripetal force necessary for 
making the turn. 

The formula for calculating the angle at 
which a curve should be banked takes into 
account the car’s speed and the angle of the 
curve, but does not include the mass of the vehi- 
cle itself. As a result, highway departments post 
signs stating the speed at which vehicles should 
make the turn, but these signs do not need to 
include specific statements regarding the weight 
of given models. 

The Centrifuge 

To return to the subject of “centrifugal force” — 
which, as noted earlier, is really just centrifugal 
motion — you might ask, “If there is no such thing 
as centrifugal force, how does a centrifuge work?” 
Used widely in medicine and a variety of sciences, 
a centrifuge is a device that separates particles 
within a liquid. One application, for instance, is 
to separate red blood cells from plasma. 

Typically a centrifuge consists of a base; a 
rotating tube perpendicular to the base; and two 
vials attached by movable centrifuge arms to the 


4B 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


rotating tube. The movable arms are hinged at 
the top of the rotating tube, and thus can move 
upward at an angle approaching 90° to the tube. 
When the tube begins to spin, centripetal force 
pulls the material in the vials toward the center. 

Materials that are denser have greater iner- 
tia, and thus are less responsive to centripetal 
force. Hence, they seem to be pushed outward, 
but in fact what has happened is that the less 
dense material has been pulled inward. This leads 
to the separation of components, for instance, 
with plasma on the top and red blood cells on the 
bottom. Again, the plasma is not as dense, and 
thus is more easily pulled toward the center of 
rotation, whereas the red blood cells respond less, 
and consequently remain on the bottom. 

The centrifuge was invented in 1883 by Carl 
de Laval (1845-1913), a Swedish engineer, who 
used it to separate cream from milk. During the 
1920s, the chemist Theodor Svedberg (1884- 
1971), who was also Swedish, improved on 
Laval’s work to create the ultracentrifuge, used 
for separating very small particles of similar 
weight. 

In a typical ultracentrifuge, the vials are no 
larger than 0.2 in (0.6 cm) in diameter, and these 
may rotate at speeds of up to 230,000 revolutions 
per minute. Most centrifuges in use by industry 
rotate in a range between 1,000 and 15,000 revo- 
lutions per minute, but others with scientific 
applications rotate at a much higher rate, and can 
produce a force more than 25,000 times as great 
as that of gravity. 

In 1994, researchers at the University of Col- 
orado created a sort of super-centrifuge for sim- 
ulating stresses applied to dams and other large 
structures. The instrument has just one cen- 
trifuge arm, measuring 19.69 ft (6 m), attached 
to which is a swinging basket containing a scale 
model of the structure to be tested. If the model 
is 1/50 the size of the actual structure, then the 
centrifuge is set to create a centripetal force 50 
times that of gravity. 

The Colorado centrifuge has also been used 
to test the effects of explosions on buildings. 
Because the combination of forces — centripetal, 
gravity, and that of the explosion itself — is so 
great, it takes a very small quantity of explosive to 
measure the effects of a blast on a model of the 
building. 


Industrial uses of the centrifuge include that 
for which Laval invented it — separation of cream 
from milk — as well as the separation of impuri- 
ties from other substances. Water can be removed 
from oil or jet fuel with a centrifuge, and like- 
wise, waste-management agencies use it to sepa- 
rate solid materials from waste water prior to 
purifying the water itself. 

Closer to home, a washing machine on spin 
cycle is a type of centrifuge. As the wet clothes 
spin, the water in them tends to move outward, 
separating from the clothes themselves. An even 
simpler, more down-to-earth centrifuge can be 
created by tying a fairly heavy weight to a rope 
and swinging it above one’s head: once again, the 
weight behaves as though it were pushed outward, 
though in fact, it is only responding to inertia. 

Roller Coasters and Cen- 
tripetal Force 

People ride roller coasters, of course, for the thrill 
they experience, but that thrill has more to do 
with centripetal force than with speed. By the 
late twentieth century, roller coasters capable 
of speeds above 90 MPH (144 km/h) began to 
appear in amusement parks around America; but 
prior to that time, the actual speeds of a roller 
coaster were not particularly impressive. Seldom, 
if ever, did they exceed that of a car moving down 
the highway. On the other hand, the acceleration 
and centripetal force generated on a roller coast- 
er are high, conveying a sense of weightlessness 
(and sometimes the opposite of weightlessness) 
that is memorable indeed. 

Few parts of a roller coaster ride are straight 
and flat — usually just those segments that mark 
the end of one ride and the beginning of anoth- 
er. The rest of the track is generally composed of 
dips and hills, banked turns, and in some cases, 
clothoid loops. The latter refers to a geometric 
shape known as a clothoid, rather like a teardrop 
upside-down. 

Because of its shape, the clothoid has a much 
smaller radius at the top than at the bottom — a 
key factor in the operation of the roller coaster 
ride through these loops. In days past, roller- 
coaster designers used perfectly circular loops, 
which allowed cars to enter them at speeds that 
were too high, built too much force and resulted 
in injuries for riders. Eventually, engineers recog- 
nized the clothoid as a means of providing a safe, 
fun ride. 


Centripetal 

Force 


49 


SCIENCE OF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


Centripetal 

Force 


KEY TERMS 


acceleration: A change in velocity. 

centrifugal: A term describing the 

tendency of objects in uniform circular 
motion to move away from the center of 
the circular path. Though the term “cen- 
trifugal force” is often used, it is inertia, 
rather than force, that causes the object to 
move outward. 

centripetal force: The force 

that causes an object in uniform circular 
motion to move toward the center of the 
circular path. 

inertia: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

mas s : A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. 

scalar: A quantity that possesses 

only magnitude, with no specific direction. 


Mass, time, and speed are all scalars. A 
scalar is contrasted with a vector. 

speed: The rate at which the position 

of an object changes over a given period of 
time. 

tangential: Movement along a tan- 

gent, or a line that touches a circle at just 
one point and does not intersect the circle. 

UNIFORM CIRCULAR MGTIDN: 

The motion of an object around the center 
of a circle in such a manner that speed is 
constant or unchanging. 

vectgr: A quantity that possesses 

both magnitude and direction. Velocity, 
acceleration, and weight (which involves 
the downward acceleration due to gravity) 
are examples of vectors. It is contrasted 
with a scalar. 

velocity: The speed of an object in a 

particular direction. 


5D 


As you move into the clothoid loop, then up, 
then over, and down, you are constantly chang- 
ing position. Speed, too, is changing. On the way 
up the loop, the roller coaster slows due to a 
decrease in kinetic energy, or the energy that an 
object possesses by virtue of its movement. At the 
top of the loop, the roller coaster has gained a 
great deal of potential energy, or the energy an 
object possesses by virtue of its position, and its 
kinetic energy is at zero. But once it starts going 
down the other side, kinetic energy — and with it 
speed — increases rapidly once again. 

Throughout the ride, you experience two 
forces, gravity, or weight, and the force (due to 
motion) of the roller coaster itself, known as 
normal force. Like kinetic and potential energy — 
which rise and fall correspondingly with dips and 
hills — normal force and gravitational force are 
locked in a sort of “competition” throughout the 
roller-coaster rider. For the coaster to have its 

VDLUME z: REAL-LIFE PHYSICS 


proper effect, normal force must exceed that of 
gravity in most places. 

The increase in normal force on a roller- 
coaster ride can be attributed to acceleration and 
centripetal motion, which cause you to experi- 
ence something other than gravity. Hence, at the 
top of a loop, you feel lighter than normal, and at 
the bottom, heavier. In fact, there has been no 
real change in your weight: it is, like the idea of 
“centrifugal force” discussed earlier, a matter of 
perception. 

WHERE T □ LEARN MDRE 

Aylesworth, Thomas G. Science at the Ball Game. New 
York: Walker, 1977. 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Buller, Laura and Ron Taylor. Forces of Nature. Illustra- 
tions by John Hutchinson and Stan North. New York: 
Marshall Cavendish, 1990. 

SCIENCE GF EVERYDAY THINGS 



“Centrifugal Force — Rotational Motion.” National Aero- 
nautics and Space Administration (Web site). 
<http://observe.iw.nasa.gov/nasa/space/centrifugal/ 
centrifugal3.html> (March 5, 2001). 

“Circular and Satellite Motion” (Web site). 

<http://www.glenbrook.kl2.il.us/gbssci/phys/Class/ 
circles/circtoc.html> (March 5, 2001). 

Cobb, Vicki. Why Doesn’t the Earth Fall Up? And Other 
Not Such Dumb Questions About Motion. Illustrated 
by Ted Enik. New York: Lodestar Books, 1988. 

Lefkowitz, R. J. Push! Pull! Stop! Go! A Book About Forces 


and Motion. Illustrated by June Goldsborough. New 
York: Parents’ Magazine Press, 1975. 

“Rotational Motion.” Physics Department, University of 
Guelph (Web site). 

<http://www.physics.uoguelph.ca/tutorials/torque/> 
(March 4, 2001). 

Schaefer, Lola M. Circular Movement. Mankato, MN: 
Pebble Books, 2000. 

Snedden, Robert. Forces. Des Plaines, IL: Heinemann 
Library, 1999. 

Whyman, Kathryn. Forces in Action. New York: Glouces- 
ter Press, 1986. 


Centripetal 

Force 


5 1 


SCIENCE OF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


F R I C T I □ N 


52 


C □ N C E PT 

Friction is the force that resists motion when the 
surface of one object comes into contact with the 
surface of another. In a machine, friction reduces 
the mechanical advantage, or the ratio of output 
to input: an automobile, for instance, uses one- 
quarter of its energy on reducing friction. Yet, it 
is also friction in the tires that allows the car to 
stay on the road, and friction in the clutch that 
makes it possible to drive at all. From matches to 
machines to molecular structures, friction is one 
of the most significant phenomena in the physi- 
cal world. 


H □ W IT WDRKS 

The definition of friction as “the force that resists 
motion when the surface of one object comes 
into contact with the surface of another” does 
not exactly identify what it is. Rather, the state- 
ment describes the manifestation of friction in 
terms of how other objects respond. A less 
sophisticated version of such a definition would 
explain electricity, for instance, as “the force that 
runs electrical appliances.” The reason why fric- 
tion cannot be more firmly identified is simple: 
physicists do not fully understand what it is. 

Much the same could be said of force, 
defined by Sir Isaac Newton’s (1642-1727) sec- 
ond law of motion as the product of mass multi- 
plied acceleration. The fact is that force is so fun- 
damental that it defies full explanation, except in 
terms of the elements that compose it, and com- 
pared to force, friction is relatively easy to identi- 
fy. In fact, friction plays a part in the total force 
that must be opposed in order for movement to 
take place in many situations. So, too, does grav- 

VDLUME 2: REAL-LIFE PHYSICS 


ity — and gravity, unlike force itself, is much easi- 
er to explain. Since gravity plays a role in friction, 
it is worthwhile to review its essentials. 

Newton’s first law of motion identifies iner- 
tia, a tendency of objects in the physical universe 
that is sometimes mistaken for friction. When an 
object is in motion or at rest, the first law states, 
it will remain in that state at a constant velocity 
(which is zero for an object at rest) unless or until 
an outside force acts on it. This tendency to 
remain in a given state of motion is inertia. 

Inertia is not a force: on the contrary, a very 
small quantity of force may accelerate an object, 
thus overcoming its inertia. Inertia is, however, a 
component of force, since mass is a measure of 
inertia. In the case of gravitational force, mass is 
multiplied by the acceleration due to gravity, 
which is equal to 32 ft (9.8 m)/sec 2 . People in 
everyday life are familiar with another term for 
gravitational force: weight. 

Weight, in turn, is an all-important factor in 
friction, as revealed in the three laws governing 
the friction between an object at rest and the sur- 
face on which it sits. According to the first of 
these, friction is proportional to the weight of the 
object. The second law states that friction is not 
determined by the surface area of the object — 
that is, the area that touches the surface on which 
the object rests. In fact, the contact area between 
object and surface is a dependant variable, a 
function of weight. 

The second law might seem obvious if one 
were thinking of a relatively elastic object — say, a 
garbage bag filled with newspapers sitting on the 
finished concrete floor of a garage. Clearly as 
more newspapers are added, thus increasing the 

SCIENCE □ F EVERYDAY THINGS 



weight, its surface area would increase as well. 
But what if one were to compare a large card- 
board box (the kind, for instance, in which tele- 
visions or computers are shipped) with an ordi- 
nary concrete block of the type used in founda- 
tions for residential construction? Obviously, the 
block has more friction against the concrete 
floor; but at the same time, it is clear that despite 
its greater weight, the block has less surface area 
than the box. How can this be? 

The answer is that “surface area” is quite lit- 
erally more than meets the eye. Friction itself 
occurs at a level invisible to the naked eye, and 
involves the adhesive forces between molecules 
on surfaces pushed together by the force of 
weight. This is similar to the manner in which, 
when viewed through a high-powered lens, two 
complementary patches of Velcro™ are revealed 
as a forest of hooks on the one hand, and a sea of 
loops on the other. 

On a much more intensified level, that of 
molecular structure, the surfaces of objects 
appear as mountains and valleys. Nothing, in 
fact, is smooth when viewed on this scale, and 
hence, from a molecular perspective, it becomes 
clear that two objects in contact actually touch 
one another only in places. An increase of weight, 
however, begins pushing objects together, caus- 
ing an increase in the actual — that is, the molec- 
ular — area of contact. Hence area of contact is 
proportional to weight. 

Just as the second law regarding friction states 
that surface area does not determine friction (but 
rather, weight determines surface area), the third 
law holds that friction is independent of the speed 
at which an object is moving along a surface — 
provided that speed is not zero. The reason for 
this provision is that an object with no speed (that 
is, one standing perfectly still) is subject to the 
most powerful form of friction, static friction. 

The latter is the friction that an object at rest 
must overcome to be set in motion; however, this 
should not be confused with inertia, which is rel- 
atively easy to overcome through the use of force. 
Inertia, in fact, is far less complicated than static 
friction, involving only mass rather than weight. 
Nor is inertia affected by the composition of the 
materials touching one another. 

As stated earlier, friction is proportional to 
weight, which suggests that another factor is 
involved. And indeed there is another factor, 
known as coefficient of friction. The latter, desig- 

SCIENCE □ E EVERYDAY THINGS 



The raised tread on an automobile’s tires, cou- 
pled WITH THE ROUGHENED ROAD SURFACE, PROVIDES 
SUFFICIENT FRICTION FOR THE DRIVER TO BE ABLE TO 

turn the car and to stop. (Photograph by Martyn God- 
dard/Corbis. Reproduced by permission.) 

nated by the Greek letter mu (jt), is constant for 
any two types of surface in contact with one 
another, and provides a means of comparing the 
friction between them to that between other sur- 
faces. For instance, the coefficient of static fric- 
tion for wood on wood is 0.5; but for metal on 
metal with lubrication in between, it is only 0.03. 
A rubber tire on dry concrete yields the highest 
coefficient of static friction, 1.0, which is desir- 
able in that particular situation. 

Coefficients are much lower for the second 
type of friction, sliding friction, the frictional 
resistance experienced by a body in motion. 
Whereas the earlier figures measured the relative 
resistance to putting certain objects into motion, 
the sliding-friction coefficient indicates the rela- 
tive resistance against those objects once they are 
moving. To use the same materials mentioned 
above, the coefficient of sliding friction for wood 
on wood is 0.3; for two lubricated metals 0.03 (no 
change); and for a rubber tire on dry concrete 0.7. 

Finally, there is a third variety of friction, 
one in which coefficients are so low as to be neg- 

VDLUME 2: REAL-LIFE PHYSICS 


FRICTION 


53 



Frictidn 


REAL-LIFE 
A P P L I C AT I □ N S 


54 



Actor Jack Buchanan lit this match using a sim- 
ple DISPLAY OF FRICTION: DRAGGING THE MATCH 

against the back of the matchbox. (Photograph by Hul- 
ton-Deutsch Collection/Corbis. Reproduced by permission.) 


ligible: rolling friction, or the frictional resistance 
that a wheeled object experiences when it rolls 
over a relatively smooth, flat surface. In ideal cir- 
cumstances, in fact, there would be absolutely no 
resistance between a wheel and a road. However, 
there exists no ideal — that is, perfectly rigid — 
wheel or road; both objects “give” in response to 
the other, the wheel by flattening somewhat and 
the road by experiencing indentation. 

Up to this point, coefficients of friction have 
been discussed purely in comparative terms, but in 
fact, they serve a function in computing frictional 
force — that is, the force that must be overcome to 
set an object in motion, or to keep it in motion. 
Frictional force is equal to the coefficient of fric- 
tion multiplied by normal force — that is, the per- 
pendicular force that one object or surface exerts 
on another. On a horizontal plane, normal force is 
equal to gravity and hence weight. In this equa- 
tion, the coefficient of friction establishes a limit to 
frictional force: in order to move an object in a 
given situation, one must exert a force in excess of 
the frictional force that keeps it from moving. 


Self-Motivation Through 
Friction 

Friction, in fact, always opposes movement; why, 
then, is friction necessary — as indeed it is — for 
walking, and for keeping a car on the road? The 
answer relates to the differences between friction 
and inertia alluded to earlier. In situations of 
static friction, it is easy to see how a person might 
confuse friction with inertia, since both serve to 
keep an object from moving. In situations of slid- 
ing or rolling friction, however, it is easier to see 
the difference between friction and inertia. 

Whereas friction is always opposed to move- 
ment, inertia is not. When an object is not mov- 
ing, its inertia does oppose movement — but 
when the object is in motion, then inertia resists 
stopping. In the absence of friction or other 
forces, inertia allows an object to remain in 
motion forever. Imagine a hockey player hitting a 
puck across a very, very large rink. Because ice 
has a much smaller coefficient of friction with 
regard to the puck than does dirt or asphalt, the 
puck will travel much further. Still, however, the 
ice has some friction, and, therefore, the puck 
will come to a stop at some point. 

Now suppose that instead of ice, the surface 
and objects in contact with it were friction- free, 
possessing a coefficient of zero. Then what would 
happen if the player hit the puck? Assuming for 
the purposes of this thought experiment, that the 
rink covered the entire surface of Earth, it would 
travel and travel and travel, ultimately going 
around the planet. It would never stop, because 
there would be no friction to stop it, and there- 
fore inertia would have free rein. 

The same would be true if one were to firm- 
ly push the hockey player with enough force 
(small in the absence of friction) to set him in 
motion: he would continue riding around the 
planet indefinitely, borne by his skates. But what 
if instead of being set in motion, the hockey play- 
er tried to set himself in motion by the action of 
his skates against the rink’s surface? 

He would be unable to move even a hair’s 
breadth. The fact is that while static friction oppos- 
es the movement of an object from a position of 
rest to a state of motion, it may — assuming it can 
be overcome to begin motion at all — be indispen- 
sable to that movement. As with the skater in per- 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



Friction 


petual motion across the rink, the absence of fric- 
tion means that inertia is “in control;” with fric- 
tion, however, it is possible to overcome inertia. 

Friction in Driving a Car 

The same principle applies to a car’s tires: if they 
were perfectly smooth — and, to make matters 
worse, the road were perfectly smooth as well — 
the vehicle would keep moving forward when the 
driver attempted to stop. For this reason, tires are 
designed with raised tread to maintain a high 
degree of friction, gripping the road tightly and 
dispersing water when the roadway is wet. 

The force of friction, in fact, pervades the 
entire operation of a car, and makes it possible 
for the tires themselves to turn. The turning 
force, or torque, that the driver exerts on the 
steering wheel is converted into forces that drive 
the tires, and these in turn use friction to provide 
traction. Between steering wheel and tires, of 
course, are a number of steps, with the engine 
rotating the crankshaft and transmitting power 
to the clutch, which applies friction to translate 
the motion of the crankshaft to the gearbox. 

When the driver of a car with a manual 
transmission presses down on the clutch pedal, 
this disengages the clutch itself. A clutch is a cir- 
cular mechanism containing (among other 
things) a pressure plate, which lifts off the clutch 
plate. As a result, the flywheel — the instrument 
that actually transmits force from the crank- 
shaft — is disengaged from the transmission 
shaft. With the clutch thus disengaged, the driver 
changes gears, and after the driver releases the 
clutch pedal, springs return the pressure plate 
and the clutch plate to their place against the fly- 
wheel. The flywheel then turns the transmission 
shaft. 

Controlled friction in the clutch makes this 
operation possible; likewise the synchromesh 
within the gearbox uses friction to bring the 
gearwheels into alignment. This is a complicated 
process, but at the heart of it is an engagement of 
gear teeth in which friction forces them to come 
to the same speed. 

Friction is also essential to stopping a car — 
not just with regard to the tires, but also with 
respect to the brakes. Whether they are disk 
brakes or drum brakes, two elements must come 
together with a force more powerful than the 
engine’s, and friction provides that needed force. 
In disk brakes, brake pads apply friction to both 

SCIENCE □ F EVERYDAY THINGS 


sides of the spinning disks, and in drum brakes, 
brake shoes transmit friction to the inside of a 
spinning drum. This braking force is then trans- 
mitted to the tires, which apply friction to the 
road and thus stop the car. 

Efficiency and Friction 

The automobile is just one among many exam- 
ples of a machine that could not operate without 
friction. The same is true of simple machines 
such as screws, as well as nails, pliers, bolts, and 
forceps. At the heart of this relationship is a par- 
adox, however, because friction inevitably 
reduces the efficiency of machines: a car, as noted 
earlier, exerts fully one-quarter of its power sim- 
ply on overcoming the force of friction both 
within its engine and from air resistance as it 
travels down the road. 

In scientific terms, efficiency or mechanical 
advantage is measured by the ratio of force out- 
put to force input. Clearly, in most situations it is 
ideal to maximize output and minimize input, 
and over the years inventors have dreamed of 
creating a mechanism — a perpetual motion 
machine — to do just that. In this idealized 
machine, one would apply a certain amount of 
energy to set it into operation, and then it would 
never stop; hence the ratio of output to input 
would be nearly infinite. 

Unfortunately, the perpetual motion 
machine is a dream every bit as elusive as the 
mythical Fountain of Youth. At least this is true 
on Earth, where friction will always cause a sys- 
tem to lose kinetic energy, or the energy of move- 
ment. No matter what the design, the machine 
will eventually lose energy and stop; however, 
this is not true in outer space, where friction is 
very small — though it still exists. In space it 
might truly be possible to set a machine in 
motion and let inertia do the rest; thus perhaps 
perpetual motion actually is more than a dream. 

It should also be noted that mechanical 
advantage is not always desirable. A screw is a 
highly inefficient machine: one puts much more 
force into screwing it in than the screw will exert 
once it is in place. Yet this is exactly the purpose 
of a screw: an “efficient” one, or one that worked 
its way back out of the place into which it had 
been screwed, would in fact be of little use. 

Once again, it is friction that provides a 
screw with its strangely efficient form of ineffi- 
ciency. Nonetheless, friction, in spite of the 

VDLUME 2: REAL-LIFE PHYSICS 


55 


Frictidn 


56 


advantages discussed above, is as undesirable as it 
is desirable. With friction, there is always some- 
thing lost; however, there is a physical law that 
energy does not simply disappear; it just changes 
form. In the case of friction, the energy that 
could go to moving the machine is instead trans- 
lated into sound — or even worse, heat. 

When Sparks Fly 

In movement involving friction, molecules 
vibrate, bringing about a rise in temperature. This 
can be easily demonstrated by simply rubbing 
one’s hands together quickly, as a person is apt to 
do when cold: heat increases. For a machine com- 
posed of metal parts, this increase in temperature 
can be disastrous, leading to serious wear and 
damage. This is why various forms of lubricant 
are applied to systems subject to friction. 

An automobile uses grease and oil, as well as 
ball bearings, which are tiny uniform balls of 
metal that imitate the behavior of oil-based sub- 
stances on a large scale. In a molecule of oil — 
whether it is a petroleum-related oil or the type 
of oil that comes from living things — positive 
and negative electrical charges are distributed 
throughout the molecule. By contrast, in water 
the positive charges are at one end of the mole- 
cule and the negative at the other. This creates a 
tight bond as the positive end of one water mol- 
ecule adheres to the negative end of another. 
With oil, the relative absence of attraction 
between molecules means that each is in effect a 
tiny ball separate from the others. The ball-like 
molecules “roll” between metal elements, provid- 
ing the buffer necessary to reduce friction. 

Yet for every statement one can make con- 
cerning friction, there is always another state- 
ment with which to counter it. Earlier it was 
noted that the wheel, because it reduced friction 
greatly, provided an enormous technological 
boost to societies. Yet long before the wheel — 
hundreds of thousands of years ago — an even 
more important technological breakthrough 
occurred when humans made a discovery that 
depended on maximizing friction: fire, or rather 
the means of making fire. Unlike the wheel, fire 
occurs in nature, and can spring from a number 
of causes, but when human beings harnessed the 
means of making fire on their own, they had to 
rely on the heat that comes from friction. 

By the early nineteenth century, inventors 
had developed an easy method of creating fire by 

VOLUME 2: REAL-LIFE PHYSICS 


using a little stick with a phosphorus tip. This 
stick, of course, is known as a match. In a strike- 
anywhere match, the head contains all the chem- 
icals needed to create a spark. To ignite this type 
of match, one need only create frictional heat by 
rubbing it against a surface, such as sandpaper, 
with a high coefficient of friction. 

The chemicals necessary for ignition in safe- 
ty matches, on the other hand, are dispersed 
between the match head and a treated strip, usu- 
ally found on the side of the matchbox or match- 
book. The chemicals on the tip and those on the 
striking surface must come into contact for igni- 
tion to occur, but once again, there must be fric- 
tion between the match head and the striking 
pad. Water reduces friction with its heavy bond, 
as it does with a car’s tires on a rainy day, which 
explains why matches are useless when wet. 

The Outer Limits of Friction 

Clearly friction is a complex subject, and the dis- 
coveries of modern physics only promise to add 
to that complexity. In a February 1999 online 
article for Physical Review Focus, Dana Macken- 
zie reported that “Engineers hope to make 
microscopic engines and gears as ordinary in our 
lives as microscopic circuits are today. But before 
this dream becomes a reality, they will have to 
deal with laws of friction that are very different 
from those that apply to ordinary-sized 
machines.” 

The earlier statement that friction is propor- 
tional to weight, in fact, applies only in the realm 
of classical physics. The latter term refers to the 
studies of physicists up to the end of the nine- 
teenth century, when the concerns were chiefly 
the workings of large objects whose operations 
could be discerned by the senses. Modern 
physics, on the other hand, focuses on atomic 
and molecular structures, and addresses physical 
behaviors that could not have been imagined 
prior to the twentieth century. 

According to studies conducted by Alan 
Burns and others at Sandia National Laborato- 
ries in Albuquerque, New Mexico, molecular 
interactions between objects in very close prox- 
imity create a type of friction involving repulsion 
rather than attraction. This completely upsets the 
model of friction understood for more than a 
century, and indicates new frontiers of discovery 
concerning the workings of friction at a molecu- 
lar level. 

SCIENCE OF EVERYDAY THINGS 


Friction 


KEY TERMS 


acceleration: A change in velocity. 

COEFFICIENT OF FRICTION: A fig- 

ure, constant for a particular pair of sur- 
faces in contact, that can be multiplied by 
the normal force between them to calculate 
the frictional force they experience. 

force: The product of mass multi- 

plied by acceleration. 

friction: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. Varieties including sliding fric- 
tion, static friction, and rolling friction. 
The degree of friction between two specif- 
ic surfaces is proportional to coefficient of 
friction. 

frictional force: The force nec- 

essary to set an object in motion, or to keep 
it in motion; equal to normal force multi- 
plied by coefficient of friction. 

i n e rti a: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. 

MECHANICAL ADVANTAGE: The 

ratio of force output to force input in a 
machine. 

ndrmal force: The perpendicular 

force with which two objects press against 


one another. On a plane without any 
incline (which would add acceleration in 
addition to that of gravity) normal force is 
the same as weight. 

rdlling frictidn: The frictional 

resistance that a circular object experiences 
when it rolls over a relatively smooth, flat 
surface. With a coefficient of friction much 
smaller than that of sliding friction, rolling 
friction involves by far the least amount 
of resistance among the three varieties of 
friction. 

sliding frictidn: The frictional 

resistance experienced by a body in 
motion. Here the coefficient of friction is 
greater than that for rolling friction, but 
less than for static friction. 

speed: The rate at which the position 

of an object changes over a given period of 
time. 

static frictidn: The frictional 

resistance that a stationary object must 
overcome before it can go into motion. Its 
coefficient of friction is greater than that of 
sliding friction, and thus largest among the 
three varieties of friction. 

velocity: The speed of an object in a 

particular direction. 

weight: A measure of the gravitational 

force on an object; the product of mass mul- 
tiplied by the acceleration due to gravity. 


WHERE T □ LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Buller, Laura and Ron Taylor. Forces of Nature. Illustra- 
tions by John Hutchinson and Stan North. New York: 
Marshall Cavendish, 1990. 

SCIENCE DF EVERYDAY THINGS 


Dixon, Malcolm and Karen Smith. Forces and Movement. 
Mankato, MN: Smart Apple Media, 1998. 

“Friction.” How Stuff Works (Web site). 

<http://www.howstuffworks.com/search/index.htm? 
words=friction> (March 8, 2001). 

“Friction and Interactions” (Web site). 

<http://www.cord.edu/ dept/physics/p 1 28/lec- 
ture99_12.html> (March 8, 2001). 


VDLUME 2: REAL-LIFE PHYSICS 


57 



Frictidn 


Levy, Matthys and Richard Panchyk. Engineering the 
City: How Infrastructure Works. Chicago: Chicago 
Review Press, 2000. 

Macaulay, David. The New Way Tltings Work. Boston: 
Houghton Mifflin, 1998. 

Mackenzie, Dana. “Friction of Molecules.” Physical Review 
Focus (Web site), <http://focus.aps.org/v3/st9.html 
(March 8, 2001). 


Rutherford, F. James; Gerald Holton; and Fletcher G. 
Watson. Project Physics. New York: Holt, Rinehart, 
and Winston, 1981. 

Skateboard Science (Web site). <http://www.exploratori- 
um.edu/skateboarding/ (March 8, 2001). 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 


5B 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


LAWS □ F M DTI □ N 


C □ N C E PT 

In all the universe, there are few ideas more fun- 
damental than those expressed in the three laws 
of motion. Together these explain why it is rela- 
tively difficult to start moving, and then to stop 
moving; how much force is needed to start or 
stop in a given situation; and how one force 
relates to another. In their beauty and simplicity, 
these precepts are as compelling as a poem, and 
like the best of poetry, they identify something 
that resonates through all of life. The applica- 
tions of these three laws are literally endless: from 
the planets moving through the cosmos to the 
first seconds of a car crash to the action that takes 
place when a person walks. Indeed, the laws of 
motion are such a part of daily life that terms 
such as inertia, force, and reaction extend into 
the realm of metaphor, describing emotional 
processes as much as physical ones. 

H □ W IT WDRKS 

The three laws of motion are fundamental to 
mechanics, or the study of bodies in motion. 
These laws may be stated in a number of ways, 
assuming they contain all the components iden- 
tified by Sir Isaac Newton (1642-1727). It is on 
his formulation that the following are based: 

The Three Laws of Motion 

• First law of motion: An object at rest will 
remain at rest, and an object in motion will 
remain in motion, at a constant velocity 
unless or until outside forces act upon it. 

• Second law of motion: The net force acting 
upon an object is a product of its mass mul- 
tiplied by its acceleration. 

• Third law of motion: When one object 

SCIENCE □ F EVERYDAY THINGS 


exerts a force on another, the second object 
exerts on the first a force equal in magni- 
tude but opposite in direction. 

Laws of Man vs. Laws of 
N ATU RE 

These, of course, are not “laws” in the sense that 
people normally understand that term. Human 
laws, such as injunctions against stealing or park- 
ing in a fire lane, are prescriptive: they state how 
the world should be. Behind the prescriptive 
statements of civic law, backing them up and giv- 
ing them impact, is a mechanism — police, 
courts, and penalties — for ensuring that citizens 
obey. 

A scientific law operates in exactly the oppo- 
site fashion. Here the mechanism for ensuring 
that nature “obeys” the law comes first, and the 
“law” itself is merely a descriptive statement con- 
cerning evident behavior. With human or civic 
law, it is clearly possible to disobey: hence, the 
justice system exists to discourage disobedience. 
In the case of scientific law, disobedience is clear- 
ly impossible — and if it were not, the law would 
have to be amended. 

This is not to say, however, that scientific 
laws extend beyond their own narrowly defined 
limits. On Earth, the intrusion of outside 
forces — most notably friction — prevents objects 
from behaving perfectly according to the first law 
of motion. The common-sense definition of fric- 
tion calls to mind, for instance, the action that a 
match makes as it is being struck; in its broader 
scientific meaning, however, friction can be 
defined as any force that resists relative motion 
between two bodies in contact. 

VDLUME 2: REAL-LIFE PHYSICS 




Laws of 
Motion 



The cargo bay of the space shuttle Discovery, shown just after releasing a satellite. Dnce 

RELEASED INTO THE FRICTIONLESS VACUUM AROUND EARTH, THE SATELLITE WILL MOVE INDEFINITELY 

around Earth without need for the motive power of an engine. The planet’s gravity keeps it 

AT A FIXED HEIGHT, AND AT THAT HEIGHT, IT COULD THEORETICALLY CIRCLE EARTH FOREVER. (Corbis. Repro- 
duced by permission.) 


6 □ 


The operations of physical forces on Earth 
are continually subject to friction, and this 
includes not only dry bodies, but liquids, for 
instance, which are subject to viscosity, or inter- 
nal friction. Air itself is subject to viscosity, which 
prevents objects from behaving perfectly in 
accordance with the first law of motion. Other 
forces, most notably that of gravity, also come 
into play to stop objects from moving endlessly 
once they have been set in motion. 

The vacuum of outer space presents scien- 
tists with the most perfect natural laboratory for 
testing the first law of motion: in theory, if they 
were to send a spacecraft beyond Earth’s orbital 

VDLUME 2: REAL-LIFE PHYSICS 


radius, it would continue travelling indefinitely. 
But even this craft would likely run into another 
object, such as a planet, and would then be drawn 
into its orbit. In such a case, however, it can be 
said that outside forces have acted upon it, and 
thus the first law of motion stands. 

The orbit of a satellite around Earth illus- 
trates both the truth of the first law, as well as the 
forces that limit it. To break the force of gravity, a 
powered spacecraft has to propel the satellite into 
the exosphere. Yet once it has reached the fric- 
tionless vacuum, the satellite will move indefi- 
nitely around Earth without need for the motive 
power of an engine — it will get a “free ride,” 

SCIENCE OF EVERYDAY THINGS 


thanks to the first law of motion. Unlike the 
hypothetical spacecraft described above, howev- 
er, it will not go spinning into space, because it is 
still too close to Earth. The planet’s gravity keeps 
it at a fixed height, and at that height, it could 
theoretically circle Earth forever. 

The first law of motion deserves such partic- 
ular notice, not simply because it is the first law. 
Nonetheless, it is first for a reason, because it 
establishes a framework for describing the behav- 
ior of an object in motion. The second law iden- 
tifies a means of determining the force necessary 
to move an object, or to stop it from moving, and 
the third law provides a picture of what happens 
when two objects exert force on one another. 

The first law warrants special attention 
because of misunderstandings concerning it, 
which spawned a debate that lasted nearly twen- 
ty centuries. Aristotle (384-322 b.c.) was the first 
scientist to address seriously what is now known 
as the first law of motion, though in fact, that 
term would not be coined until about two thou- 
sand years after his death. As its title suggests, his 
Physics was a seminal work, a book in which Aris- 
totle attempted to give form to, and thus define 
the territory of, studies regarding the operation 
of physical processes. Despite the great philoso- 
pher’s many achievements, however, Physics is a 
highly flawed work, particularly with regard to 
what became known as his theory of impetus — 
that is, the phenomena addressed in the first law 
of motion. 

Aristotle’s Mistake 

According to Aristotle, a moving object requires 
a continual application of force to keep it mov- 
ing: once that force is no longer applied, it ceases 
to move. You might object that, when a ball is in 
flight, the force necessary to move it has already 
been applied: a person has thrown the ball, and it 
is now on a path that will eventually be stopped 
by the force of gravity. Aristotle, however, would 
have maintained that the air itself acts as a force 
to keep the ball in flight, and that when the ball 
drops — of course he had no concept of “gravity” 
as such — it is because the force of the air on the 
ball is no longer in effect. 

These notions might seem patently absurd 
to the modern mind, but they went virtually 
unchallenged for a thousand years. Then in the 
sixth century a.d., the Byzantine philosopher 
Johannes Philoponus (c. 490-570) wrote a cri- 

SCIENCE □ E EVERYDAY THINGS 


tique of Physics. In what sounds very much like a 
precursor to the first law of motion, Philoponus 
held that a body will keep moving in the absence 
of friction or opposition. 

He further maintained that velocity is pro- 
portional to the positive difference between force 
and resistance — in other words, that the force 
propelling an object must be greater than the 
resistance. As long as force exceeds resistance, 
Philoponus held, a body will remain in motion. 
This in fact is true: if you want to push a refriger- 
ator across a carpeted floor, you have to exert 
enough force not only to push the refrigerator, but 
also to overcome the friction from the floor itself. 

The Arab philosophers Ibn Sina (Avicenna; 
980-1037) and Ibn Bajja (Avempace; fl. c. 1100) 
defended Philoponus’s position, and the French 
scholar Peter John Olivi (1248-1298) became the 
first Western thinker to critique Aristotle’s state- 
ments on impetus. Real progress on the subject, 
however, did not resume until the time of Jean 
Buridan (1300-1358), a French physicist who 
went much further than Philoponus had eight 
centuries earlier. 

In his writing, Buridan offered an amazingly 
accurate analysis of impetus that prefigured all 
three laws of motion. It was Buridan’s position 
that one object imparts to another a certain 
amount of power, in proportion to its velocity 
and mass, that causes the second object to move 
a certain distance. This, as will be shown below, 
was amazingly close to actual fact. He was also 
correct in stating that the weight of an object 
may increase or decrease its speed, depending on 
other circumstances, and that air resistance slows 
an object in motion. 

The true breakthrough in understanding the 
laws of motion, however, came as the result of 
work done by three extraordinary men whose 
lives stretched across nearly 250 years. First came 
Nicolaus Copernicus (1473-1543), who 
advanced what was then a heretical notion: that 
Earth, rather than being the center of the uni- 
verse, revolved around the Sun along with the 
other planets. Copernicus made his case purely 
in terms of astronomy, however, with no direct 
reference to physics. 

Galileo’s Challenge: The 
Copernican Model 

Galileo Galilei (1564-1642) likewise embraced a 
heliocentric (Sun-centered) model of the uni- 

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Laws of 
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verse — a position the Church forced him to 
renounce publicly on pain of death. As a result of 
his censure, Galileo realized that in order to prove 
the Copernican model, it would be necessary to 
show why the planets remain in motion as they 
do. In explaining this, he coined the term inertia 
to describe the tendency of an object in motion to 
remain in motion, and an object at rest to remain 
at rest. Galileo’s observations, in fact, formed the 
foundation for the laws of motion. 

In the years that followed Galileo’s death, 
some of the world’s greatest scientific minds 
became involved in the effort to understand the 
forces that kept the planets in motion around the 
Sun. Among them were Johannes Kepler (1571- 
1630), Robert Hooke (1635-1703), and Edmund 
Halley (1656-1742). As a result of a dispute 
between Hooke and Sir Christopher Wren (1632- 
1723) over the subject, Halley brought the ques- 
tion to his esteemed friend Isaac Newton. As it 
turned out, Newton had long been considering 
the possibility that certain laws of motion exist- 
ed, and these he presented in definitive form in 
his Principia (1687). 

The impact of the Newton’s book, which 
included his observations on gravity, was nothing 
short of breathtaking. For the next three centuries, 
human imagination would be ruled by the New- 
tonian framework, and only in the twentieth cen- 
tury would the onset of new ideas reveal its limita- 
tions. Yet even today, outside the realm of quan- 
tum mechanics and relativity theory — in other 
words, in the world of everyday experience — 
Newton’s laws of motion remain firmly in place. 

REAL-LIFE 
A P P L I C AT I □ N S 

The First Law of Motion in a 
Car Crash 

It is now appropriate to return to the first law of 
motion, as formulated by Newton: an object 
at rest will remain at rest, and an object in motion 
will remain in motion, at a constant velocity unless 
or until outside forces act upon it. Examples of this 
first law in action are literally unlimited. 

One of the best illustrations, in fact, involves 
something completely outside the experience of 
Newton himself: an automobile. As a car moves 
down the highway, it has a tendency to remain in 
motion unless some outside force changes its 

VDLUME 2: REAL-LIFE PHYSICS 


velocity. The latter term, though it is commonly 
understood to be the same as speed, is in fact 
more specific: velocity can be defined as the 
speed of an object in a particular direction. 

In a car moving forward at a fixed rate of 60 
MPH (96 km/h), everything in the car — driver, 
passengers, objects on the seats or in the trunk — 
is also moving forward at the same rate. If that 
car then runs into a brick wall, its motion will be 
stopped, and quite abruptly. But though its 
motion has stopped, in the split seconds after the 
crash it is still responding to inertia: rather than 
bouncing off the brick wall, it will continue 
plowing into it. 

What, then, of the people and objects in the 
car? They too will continue to move forward in 
response to inertia. Though the car has been 
stopped by an outside force, those inside experi- 
ence that force indirectly, and in the fragment of 
time after the car itself has stopped, they contin- 
ue to move forward — unfortunately, straight into 
the dashboard or windshield. 

It should also be clear from this example 
exactly why seatbelts, headrests, and airbags in 
automobiles are vitally important. Attorneys may 
file lawsuits regarding a client’s injuries from 
airbags, and homespun opponents of the seatbelt 
may furnish a wealth of anecdotal evidence con- 
cerning people who allegedly died in an accident 
because they were wearing seatbelts; nonetheless, 
the first law of motion is on the side of these pro- 
tective devices. 

The admittedly gruesome illustration of a 
car hitting a brick wall assumes that the driver 
has not applied the brakes — an example of an 
outside force changing velocity — or has done so 
too late. In any case, the brakes themselves, if 
applied too abruptly, can present a hazard, and 
again, the significant factor here is inertia. Like 
the brick wall, brakes stop the car, but there is 
nothing to stop the driver and/or passengers. 
Nothing, that is, except protective devices: the 
seat belt to keep the person’s body in place, the 
airbag to cushion its blow, and the headrest to 
prevent whiplash in rear-end collisions. 

Inertia also explains what happens to a car 
when the driver makes a sharp, sudden turn. 
Suppose you are is riding in the passenger seat of 
a car moving straight ahead, when suddenly the 
driver makes a quick left turn. Though the car’s 
tires turn instantly, everything in the vehicle — its 
frame, its tires, and its contents — is still respond- 

SCIENCE OF EVERYDAY THINGS 



When a vehicle hits a wall, as shown here in a crash test, its motion will be stopped, and quite abrupt- 
ly. But though its motion has stopped, in the split seconds after the crash it is still responding to 
inertia: rather than bouncing off the brick wall, it will continue plowing into it. (Photograph by Tim 
Wright/Corbis. Reproduced by permission.) 


ing to inertia, and therefore “wants” to move for- 
ward even as it is turning to the left. 

As the car turns, the tires may respond to this 
shift in direction by squealing: their rubber sur- 
faces were moving forward, and with the sudden 
turn, the rubber skids across the pavement like a 
hard eraser on fine paper. The higher the original 
speed, of course, the greater the likelihood the tires 
will squeal. At very high speeds, it is possible the 
car may seem to make the turn “on two wheels” — 
that is, its two outer tires. It is even possible that 
the original speed was so high, and the turn so 
sharp, that the driver loses control of the car. 

Here inertia is to blame: the car simply can- 
not make the change in velocity (which, again, 
refers both to speed and direction) in time. Even 
in less severe situations, you are likely to feel that 
you have been thrown outward against the rider’s 
side door. But as in the car-and-brick-wall illus- 
tration used earlier, it is the car itself that first 
experiences the change in velocity, and thus it 
responds first. You, the passenger, then, are mov- 
ing forward even as the car has turned; therefore, 
rather than being thrown outward, you are sim- 
ply meeting the leftward-moving door even as 
you push forward. 

SCIENCE □ E EVERYDAY THINGS 


Frdm Parlor Tricks to Space 
Ships 

It would be wrong to conclude from the car- 
related illustrations above that inertia is always 
harmful. In fact it can help every bit as much as 
it can potentially harm, a fact shown by two quite 
different scenarios. 

The beneficial quality to the first scenario 
may be dubious: it is, after all, a mere parlor trick, 
albeit an entertaining one. In this famous stunt, 
with which most people are familiar even if they 
have never seen it, a full table setting is placed on 
a table with a tablecloth, and a skillful practition- 
er manages to whisk the cloth out from under the 
dishes without upsetting so much as a glass. To 
some this trick seems like true magic, or at least 
sleight of hand; but under the right conditions, it 
can be done. (This information, however, carries 
with it the warning, “Do not try this at home!”) 

To make the trick work, several things must 
align. Most importantly, the person doing it has 
to be skilled and practiced at performing the feat. 
On a physical level, it is best to minimize the fric- 
tion between the cloth and settings on the one 
hand, and the cloth and table on the other. It is 
also important to maximize the mass (a property 

VDLUME 2: REAL-LIFE PHYSICS 


63 



Laws of 
Motion 


64 


that will be discussed below) of the table settings, 
thus making them resistant to movement. Hence, 
inertia — which is measured by mass — plays a key 
role in making the tablecloth trick work. 

You might question the value of the table- 
cloth stunt, but it is not hard to recognize the 
importance of the inertial navigation system 
(INS) that guides planes across the sky. Prior to 
the 1970s, when INS made its appearance, navi- 
gation techniques for boats and planes relied on 
reference to external points: the Sun, the stars, 
the magnetic North Pole, or even nearby areas of 
land. This created all sorts of possibilities for 
error: for instance, navigation by magnet (that is, 
a compass) became virtually useless in the polar 
regions of the Arctic and Antarctic. 

By contrast, the INS uses no outside points 
of reference: it navigates purely by sensing the 
inertial force that results from changes in veloci- 
ty. Not only does it function as well near the poles 
as it does at the equator, it is difficult to tamper 
with an INS, which uses accelerometers in a 
sealed, shielded container. By contrast, radio sig- 
nals or radar can be “confused” by signals from 
the ground — as, for instance, from an enemy 
unit during wartime. 

As the plane moves along, its INS measures 
movement along all three geometrical axes, and 
provides a continuous stream of data regarding 
acceleration, velocity, and displacement. Thanks 
to this system, it is possible for a pilot leaving Cal- 
ifornia for Japan to enter the coordinates of a half- 
dozen points along the plane’s flight path, and let 
the INS guide the autopilot the rest of the way. 

Yet INS has its limitations, as illustrated by 
the tragedy that occurred aboard Korean Air 
Lines (KAL) Flight 007 on September 1, 1983. 
The plane, which contained 269 people and crew 
members, departed Anchorage, Alaska, on course 
for Seoul, South Korea. The route they would fly 
was an established one called “R-20,” and it 
appears that all the information regarding their 
flight plan had been entered correctly in the 
plane’s INS. 

This information included coordinates for 
internationally recognized points of reference, 
actually just spots on the northern Pacific with 
names such as NABIE, NUKKS, NEEVA, and so 
on, to NOKKA, thirty minutes east of Japan. Yet, 
just after passing the fishing village of Bethel, 
Alaska, on the Bering Sea, the plane started to 
veer off course, and ultimately wandered into 

VDLUME 2: REAL-LIFE PHYSICS 


Soviet airspace over the Kamchatka Peninsula 
and later Sakhalin Island. There a Soviet Su-15 
shot it down, killing all the plane’s passengers. 

In the aftermath of the Flight 007 shoot- 
down, the Soviets accused the United States and 
South Korea of sending a spy plane into their air- 
space. (Among the passengers was Larry McDon- 
ald, a staunchly anti-Communist Congressman 
from Georgia.) It is more likely, however, that the 
tragedy of 007 resulted from errors in navigation 
which probably had something to do with the 
INS. The fact is that the R-20 flight plan had been 
designed to keep aircraft well out of Soviet air- 
space, and at the time KAL 007 passed over Kam- 
chatka, it should have been 200 mi (320 km) to 
the east — over the Sea of Japan. 

Among the problems in navigating a 
transpacific flight is the curvature of the Earth, 
combined with the fact that the planet continues 
to rotate as the aircraft moves. On such long 
flights, it is impossible to “pretend,” as on a short 
flight, that Earth is flat: coordinates have to be 
adjusted for the rounded surface of the planet. In 
addition, the flight plan must take into account 
that (in the case of a flight from California to 
Japan), Earth is moving eastward even as the 
plane moves westward. The INS aboard KAL 007 
may simply have failed to correct for these fac- 
tors, and thus the error compounded as the plane 
moved further. In any case, INS will eventually be 
rendered obsolete by another form of navigation 
technology: the global positioning satellite (GPS) 
system. 

Understanding Inertia 

From examples used above, it should be clear 
that inertia is a more complex topic than you 
might immediately guess. In fact, inertia as a 
process is rather straightforward, but confusion 
regarding its meaning has turned it into a com- 
plicated subject. 

In everyday terminology, people typically 
use the word inertia to describe the tendency of a 
stationary object to remain in place. This is par- 
ticularly so when the word is used metaphorical- 
ly: as suggested earlier, the concept of inertia, like 
numerous other aspects of the laws of motion, is 
often applied to personal or emotional processes 
as much as the physical. Hence, you could say, for 
instance, “He might have changed professions 
and made more money, but inertia kept him at 
his old job.” Yet you could just as easily say, for 

SCIENCE OF EVERYDAY THINGS 


example, “He might have taken a vacation, but 
inertia kept him busy.” Because of the misguided 
way that most people use the term, it is easy to 
forget that “inertia” equally describes a tendency 
toward movement or nonmovement: in terms of 
Newtonian mechanics, it simply does not matter. 

The significance of the clause “unless or 
until outside forces act upon it” in the first law 
indicates that the object itself must be in equilib- 
rium — that is, the forces acting upon it must be 
balanced. In order for an object to be in equilib- 
rium, its rate of movement in a given direction 
must be constant. Since a rate of movement 
equal to 0 is certainly constant, an object at rest is 
in equilibrium, and therefore qualifies; but also, 
any object moving in a constant direction at a 
constant speed is also in equilibrium. 

The Second Law: Force, 

Mass, Acceleration 

As noted earlier, the first law of motion deserves 
special attention because it is the key to unlock- 
ing the other two. Having established in the first 
law the conditions under which an object in 
motion will change velocity, the second law pro- 
vides a measure of the force necessary to cause 
that change. 

Understanding the second law requires 
defining terms that, on the surface at least, seem 
like a matter of mere common sense. Even iner- 
tia requires additional explanation in light of 
terms related to the second law, because it would 
be easy to confuse it with momentum. 

The measure of inertia is mass, which 
reflects the resistance of an object to a change in 
its motion. Weight, on the other hand, measures 
the gravitational force on an object. (The concept 
of force itself will require further definition 
shortly.) Hence a person’s mass is the same every- 
where in the universe, but their weight would dif- 
fer from planet to planet. 

This can get somewhat confusing when you 
attempt to convert between English and metric 
units, because the pound is a unit of weight or 
force, whereas the kilogram is a unit of mass. In 
fact it would be more appropriate to set up kilo- 
grams against the English unit called the slug 
(equal to 14.59 kg), or to compare pounds to the 
metric unit of force, the newton (N), which is 
equal to the acceleration of one meter per second 
per second on an object of 1 kg in mass. 

SCIENCE □ E EVERYDAY THINGS 


Hence, though many tables of weights and 
measures show that 1 kg is equal to 2.21 lb, this is 
only true at sea level on Earth. A person with a 
mass of 100 kg on Earth would have the same 
mass on the Moon; but whereas he might weigh 
221 lb on Earth, he would be considerably lighter 
on the Moon. In other words, it would be much 
easier to lift a 221-lb man on the Moon than on 
Earth, but it would be no easier to push him 
aside. 

To return to the subject of momentum, 
whereas inertia is measured by mass, momentum 
is equal to mass multiplied by velocity. Hence 
momentum, which Newton called “quantity of 
motion,” is in effect inertia multiplied by veloci- 
ty. Momentum is a subject unto itself; what mat- 
ters here is the role that mass (and thus inertia) 
plays in the second law of motion. 

According to the second law, the net force 
acting upon an object is a product of its mass 
multiplied by its acceleration. The latter is 
defined as a change in velocity over a given time 
interval: hence acceleration is usually presented 
in terms of “feet (or meters) per second per sec- 
ond” — that is, feet or meters per second squared. 
The acceleration due to gravity is 32 ft (9.8 m) 
per second per second, meaning that as every sec- 
ond passes, the speed of a falling object is 
increasing by 32 ft (9.8 m) per second. 

The second law, as stated earlier, serves to 
develop the first law by defining the force neces- 
sary to change the velocity of an object. The law 
was integral to the confirming of the Copernican 
model, in which planets revolve around the Sun. 
Because velocity indicates movement in a single 
(straight) direction, when an object moves in a 
curve — as the planets do around the Sun — it is 
by definition changing velocity, or accelerating. 
The fact that the planets, which clearly possessed 
mass, underwent acceleration meant that some 
force must be acting on them: a gravitational pull 
exerted by the Sun, most massive object in the 
solar system. 

Gravity is in fact one of four types of force at 
work in the universe. The others are electromag- 
netic interactions, and “strong” and “weak” 
nuclear interactions. The other three were 
unknown to Newton — yet his definition of force 
is still applicable. Newton’s calculation of gravi- 
tational force (which, like momentum, is a sub- 
ject unto itself) made it possible for Halley to 
determine that the comet he had observed in 

VDLUME 2: REAL-LIFE PHYSICS 


LAWS DF 
MDTIDN 


65 


Laws of 
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66 


1682 — the comet that today bears his name — 
would reappear in 1758, as indeed it has for every 
75-76 years since then. Today scientists use the 
understanding of gravitational force imparted by 
Newton to determine the exact altitude necessary 
for a satellite to remain stationary above the same 
point on Earth’s surface. 

The second law is so fundamental to the 
operation of the universe that you seldom notice 
its application, and it is easiest to illustrate by 
examples such as those above — of astronomers 
and physicists applying it to matters far beyond 
the scope of daily life. Yet the second law also 
makes it possible, for instance, to calculate the 
amount of force needed to move an object, and 
thus people put it into use every day without 
knowing that they are doing so. 

The Third Law: Action and 
Reaction 

As with the second law, the third law of motion 
builds on the first two. Having defined the force 
necessary to overcome inertia, the third law pre- 
dicts what will happen when one force comes 
into contact with another force. As the third law 
states, when one object exerts a force on another, 
the second object exerts on the first a force equal 
in magnitude but opposite in direction. 

Unlike the second law, this one is much eas- 
ier to illustrate in daily life. If a book is sitting on 
a table, that means that the book is exerting a 
force on the table equal to its mass multiplied by 
its rate of acceleration. Though it is not moving, 
the book is subject to the rate of gravitational 
acceleration, and in fact force and weight (which 
is defined as mass multiplied by the rate of accel- 
eration due to gravity) are the same. At the same 
time, the table pushes up on the book with an 
exactly equal amount of force — just enough to 
keep it stationary. If the table exerted more force 
that the book — in other words, if instead of 
being an ordinary table it were some sort of 
pneumatic press pushing upward — then the 
book would fly off the table. 

There is no such thing as an unpaired force 
in the universe. The table rests on the floor just as 
the book rests on it, and the floor pushes up on 
the table with a force equal in magnitude to that 
with which the table presses down on the floor. 
The same is true for the floor and the supporting 
beams that hold it up, and for the supporting 

VDLUME 2: REAL-LIFE PHYSICS 


beams and the foundation of the building, and 
the building and the ground, and so on. 

These pairs of forces exist everywhere. When 
you walk, you move forward by pushing back- 
ward on the ground with a force equal to your 
mass multiplied by your rate of downward grav- 
itational acceleration. (This force, in other words, 
is the same as weight.) At the same time, the 
ground actually pushes back with an equal force. 
You do not perceive the fact that Earth is pushing 
you upward, simply because its enormous mass 
makes this motion negligible — but it does push. 

If you were stepping off of a small 
unmoored boat and onto a dock, however, some- 
thing quite different would happen. The force of 
your leap to the dock would exert an equal force 
against the boat, pushing it further out into the 
water, and as a result, you would likely end up in 
the water as well. Again, the reaction is equal and 
opposite; the problem is that the boat in this 
illustration is not fixed in place like the ground 
beneath your feet. 

Differences in mass can result in apparently 
different reactions, though in fact the force is the 
same. This can be illustrated by imagining a 
mother and her six-year-old daughter skating on 
ice, a relatively frictionless surface. Facing one 
another, they push against each other, and as a 
result each moves backward. The child, of course, 
will move backward faster because her mass is 
less than that of her mother. Because the force 
they exerted is equal, the daughter’s acceleration 
is greater, and she moves farther. 

Ice is not a perfectly frictionless surface, of 
course: otherwise, skating would be impossible. 
Likewise friction is absolutely necessary for walk- 
ing, as you can illustrate by trying to walk on a 
perfectly slick surface — for instance, a skating 
rink covered with oil. In this situation, there is 
still an equally paired set of forces — your body 
presses down on the surface of the ice with as 
much force as the ice presses upward — but the 
lack of friction impedes the physical process of 
pushing off against the floor. 

It will only be possible to overcome inertia 
by recourse to outside intervention, as for 
instance if someone who is not on the ice tossed 
out a rope attached to a pole in the ground. Alter- 
natively, if the person on the ice were carrying a 
heavy load of rocks, it would be possible to move 
by throwing the rocks backward. In this situa- 
tion, you are exerting force on the rock, and this 

SCIENCE OF EVERYDAY THINGS 


Laws df 
Motion 


KEY TERMS 


acceleration: A change in velocity 

over a given time period. 

equilibrium: A situation in which 

the forces acting upon an object are in 
balance. 

friction: Any force that resists the 

motion of body in relation to another with 
which it is in contact. 

i n e rti a: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. A 
kilogram is a unit of mass, whereas a 
pound is a unit of weight. The mass of an 
object remains the same throughout the 
universe, whereas its weight is a function of 
gravity on any given planet. 


mechanics: The study of bodies in 

motion. 

momentum: The product of mass 

multiplied by velocity. 

speed: The rate at which the position 

of an object changes over a given period 
of time. 

velocity: The speed of an object in a 

particular direction. 

viscosity: The internal friction in a 
fluid that makes it resistant to flow. 

weight: A measure of the gravitation- 

al force on an object. A pound is a unit of 
weight, whereas a kilogram is a unit of 
mass. Weight thus would change from 
planet to planet, whereas mass remains 
constant throughout the universe. 


backward force results in a force propelling the 
thrower forward. 

This final point about friction and move- 
ment is an appropriate place to close the discus- 
sion on the laws of motion. Where walking or 
skating are concerned — and in the absence of a 
bag of rocks or some other outside force — fric- 
tion is necessary to the action of creating a back- 
ward force and therefore moving forward. On the 
other hand, the absence of friction would make it 
possible for an object in movement to continue 
moving indefinitely, in line with the first law of 
motion. In either case, friction opposes inertia. 

The fact is that friction itself is a force. Thus, 
if you try to slide a block of wood across a floor, 
friction will stop it. It is important to remember 
this, lest you fall into the fallacy that bedeviled 
Aristotle’s thinking and thus confused the world 
for many centuries. The block did not stop mov- 
ing because the force that pushed it was no 
longer being applied; it stopped because an 

SCIENCE OF EVERYDAY THINGS 


opposing force, friction, was greater than the 

force that was pushing it. 

WHERE TD LEARN MORE 

Ardley, Neil. The Science Book of Motion. San Diego: 
Harcourt Brace Jovanovich, 1992. 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Chase, Sara B. Moving to Win: The Physics of Sports. New 
York: Messner, 1977. 

Fleisher, Paul. Secrets of the Universe: Discovering the Uni- 
versal Laws of Science. Illustrated by Patricia A. Keel- 
er. New York: Atheneum, 1987. 

“The Laws of Motion.” How It Flies (Web site). 
<http://www.monmouth.com/~jsd/how/htm/ 
motion.html> (February 27, 2001). 

Newton, Isaac (translated by Andrew Motte, 1729). The 
Principia (Web site). 

<http://members.tripod.com/~gravitee/principia. 
html> (February 27, 2001). 

Newton’s Laws of Motion (Web site), <http://www.glen- 
brook.kl2.il.us/gbssci/phys/Class/newtlaws/newtloc. 
html> (February 27, 2001). 


VDLUME z: REAL-LIFE PHYSICS 


67 




Laws of 
Motion 


“Newton’s Laws of Motion.” Dryden Flight Research Cen- 
ter, National Aeronautics and Space Administration 
(NASA) (Web site), <http://www.dfrc.nasa.gov/ 
trc/saic/newton.html> (February 27, 2001). 

“Newton’s Laws of Motion: Movin’ On.” Beyond Books 


(Web site). <http://www.beyondbooks. 
com/psc91/4.asp> (February 27, 2001). 

Roberts, Jeremy. How Do We Know the Laws of Motion? 
New York: Rosen, 2001. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 


63 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


G R AV I T Y AND 
G R AV I TAT I □ N 


C □ N C E PT 

Gravity is, quite simply, the force that holds 
together the universe. People are accustomed to 
thinking of it purely in terms of the gravitational 
pull Earth exerts on smaller bodies — a stone, a 
human being, even the Moon — or perhaps in 
terms of the Sun’s gravitational pull on Earth. In 
fact, everything exerts a gravitational attraction 
toward everything else, an attraction commensu- 
rate with the two body’s relative mass, and 
inversely related to the distance between them. 
The earliest awareness of gravity emerged in 
response to a simple question: why do objects fall 
when released from any restraining force? The 
answers, which began taking shape in the six- 
teenth century, were far from obvious. In mod- 
ern times, understanding of gravitational force 
has expanded manyfold: gravity is clearly a law 
throughout the universe — yet some of the more 
complicated questions regarding gravitational 
force are far from settled. 

H □ W IT WDRKS 

Aristotle’s Model 

Greek philosophers of the period from the sixth 
to the fourth century b.c. grappled with a variety 
of questions concerning the fundamental nature 
of physical reality, and the forces that bind that 
reality into a whole. Among the most advanced 
thinkers of that period was Democritus (c. 460- 
370 b.c.), who put forth a hypothesis many thou- 
sands of years ahead of its time: that all of matter 
interacts at the atomic level. 

Aristotle (384-322 B.c.), however, rejected 
the explanation offered by Democritus, an unfor- 
tunate circumstance given the fact that the great 

SCIENCE □ F EVERYDAY THINGS 


philosopher exerted an incalculable influence on 
the development of scientific thought. Aristotle’s 
contributions to the advancement of the sciences 
were many and varied, yet his influence in 
physics was at least as harmful as it was benefi- 
cial. Furthermore, the fact that intellectual 
progress began slowing after several fruitful cen- 
turies of development in Greece only com- 
pounded the error. By the time civilization had 
reached the Middle Ages (c. 500 a.d.) the Aris- 
totelian model of physical reality had been firm- 
ly established, and an entire millennium passed 
before it was successfully challenged. 

Wrong though it was in virtually all particu- 
lars, the Aristotelian system offered a comforting 
symmetry amid the troubled centuries of the 
early medieval period. It must have been reassur- 
ing indeed to believe that the physical universe 
was as simple as the world of human affairs was 
complex. According to this neat model, all mate- 
rials on Earth consisted of four elements: earth, 
water, air, and fire. 

Each element had its natural place. Hence, 
earth was always the lowest, and in some places, 
earth was covered by water. Water must then be 
higher, but clearly air was higher still, since it 
covered earth and water. Highest of all was fire, 
whose natural place was in the skies above the 
air. Reflecting these concentric circles were the 
orbits of the Sun, the Moon, and the five known 
planets. Their orbital paths, in the Aristotelian 
model of the universe — a model developed to a 
great degree by the astronomer Ptolemy (c. 100- 
170) — were actually spheres that revolved 
around Earth with clockwork precision. 

On Earth, according to the Aristotelian 
model, objects tended to fall toward the ground 
in accordance with the admixtures of differing 

VDLUME 2: REAL-LIFE PHYSICS 



Gravity and 
Gravitation 



Because of Earth’s gravity, the woman being shot out of this cannon will eventually fall 
to the ground rather than ascend into OUTER space. (Underwood & Underwood/Corbis. Reproduced by 
permission.) 


V □ 


elements they contained. A rock, for instance, 
was mostly earth, and hence it sought its own 
level, the lowest of all four elements. For the same 
reason, a burning fire rose, seeking the heights 
that were fire’s natural domain. It followed from 
this that an object falls faster or slower, depend- 
ing on the relative mixtures of elements in it: or, 
to use more modern terms, the heavier the 
object, the faster it falls. 

Galileo Takes Up the Coper- 
n i can Challenge 

Over the centuries, a small but significant body 
of scientists and philosophers — each working 
independent from the other but building on the 
ideas of his predecessors — slowly began chipping 
away at the Aristotelian framework. The pivotal 
challenge came in the early part of the century, 
and the thinker who put it forward was not a 
physicist but an astronomer: Nicolaus Coperni- 
cus (1473-1543.) 

Based on his study of the planets, Coperni- 
cus offered an entirely new model of the uni- 
verse, one that placed the Sun and not Earth at its 
center. He was not the first to offer such an idea: 
half a century after Aristotle’s death, Aristarchus 
(fl. 270 B.c.) had a similar idea, but Ptolemy 

VDLUME 2: REAL-LIFE PHYSICS 


rejected his heliocentric (Sun-centered) model in 
favor of the geocentric or Earth-centered one. In 
subsequent centuries, no less a political authori- 
ty than the Catholic Church gave its approval to 
the Ptolemaic system. This system seemed to fit 
well with a literal interpretation of biblical pas- 
sages concerning God’s relationship with man, 
and man’s relationship to the cosmos; hence, the 
heliocentric model of Copernicus constituted an 
offense to morality. 

For this reason, Copernicus was hesitant to 
defend his ideas publicly, yet these concepts 
found their way into the consciousness of Euro- 
pean thinkers, causing a paradigm shift so funda- 
mental that it has been dubbed “the Copernican 
Revolution.” Still, Copernicus offered no expla- 
nation as to why the planets behaved as they did: 
hence, the true leader of the Copernican Revolu- 
tion was not Copernicus himself but Galileo 
Galilei (1564-1642.) 

Initially, Galileo set out to study and defend 
the ideas of Copernicus through astronomy, but 
soon the Church forced him to recant. It is said 
that after issuing a statement in which he refuted 
the proposition that Earth moves — a direct 
attack on the static harmony of the Aris- 
totelian/Ptolemaic model — he protested in pri- 

SCIENCE OF EVERYDAY THINGS 


vate: “E pur si muove!” (But it does move!) Placed 
under house arrest by authorities from Rome, he 
turned his attention to an effort that, ironically, 
struck the fatal blow against the old model of the 
cosmos: a proof of the Copernican system 
according to the laws of physics. 

GRAVITATIONAL ACCELERA- 
TION. In the process of defending Copernicus, 
Galileo actually inaugurated the modern history 
of physics as a science (as opposed to what it had 
been during the Middle Ages: a nest of supposi- 
tions masquerading as knowledge). Specifically, 
Galileo set out to test the hypothesis that objects 
fall as they do, not because of their weight, but as 
a consequence of gravitational force. If this were 
so, the acceleration of falling bodies would have 
to be the same, regardless of weight. Of course, it 
was clear that a stone fell faster than a feather, but 
Galileo reasoned that this was a result of factors 
other than weight, and later investigations con- 
firmed that air resistance and friction, not 
weight, are responsible for this difference. 

On the other hand, if one drops two objects 
that have similar air resistance but differing 
weight — say, a large stone and a smaller one — 
they fall at almost exactly the same rate. To test 
this directly, however, would have been difficult 
for Galileo: stones fall so fast that, even if 
dropped from a great height, they would hit the 
ground too soon for their rate of fall to be tested 
with the instruments then available. 

Instead, Galileo used the motion of a pendu- 
lum, and the behavior of objects rolling or slid- 
ing down inclined planes, as his models. On the 
basis of his observations, he concluded that all 
bodies are subject to a uniform rate of gravita- 
tional acceleration, later calibrated at 32 ft (9.8 
m) per second. What this means is that for every 
32 ft an object falls, it is accelerating at a rate of 
32 ft per second as well; hence, after 2 seconds, it 
falls at the rate of 64 ft (19.6 m) per second; after 
3 seconds, at 96 ft (29.4 m) per second, and so on. 

Newton Discovers the Princi- 
ple of Gravity 

Building on the work of his distinguished fore- 
bear, Sir Isaac Newton (1642-1727) — who, inci- 
dentally, was born the same year Galileo died — 
developed a paradigm for gravitation that, even 
today, explains the behavior of objects in virtual- 
ly all situations throughout the universe. Indeed, 
the Newtonian model reigned until the early 



This photo shows an apple and a feather being 

DROPPED IN A VACUUM TUBE. BECAUSE OF THE 
ABSENCE OF AIR RESISTANCE, THE TWO OBJECTS FALL 

at the same rate. (Photograph by James A. Sugar/Corbis. Repro- 
duced by permission.) 

twentieth century, when Albert Einstein (1879- 
1955) challenged it on certain specifics. 

Even so, Einstein’s relativity did not disprove 
the Newtonian system as Copernicus and Galileo 
disproved Aristotle’s and Ptolemy’s theories; 
rather, it showed the limitations of Newtonian 
mechanics for describing the behavior of certain 
objects and phenomena. However, in the ordi- 
nary world of day-to-day experience — the world 
in which stones drop and heavy objects are hard 
to lift — the Newtonian system still offers the key 
to how and why things work as they do. This is 
particularly the case with regard to gravity and 
gravitation. 

Like Galileo, Newton began in part with the 
aim of testing hypotheses put forth by an 
astronomer — in this case Johannes Kepler (1571- 
1630). In the early years of the seventeenth cen- 
tury, Kepler published his three laws of planetary 
motion, which together identified the elliptical 
(oval-shaped) path of the planets around the 
Sun. Kepler had discovered a mathematical rela- 
tionship that connected the distances of the plan- 
ets from the Sun to the period of their revolution 


Gravity and 
Gravitation 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


V 1 



Gravity and 
Gravitation 


72 


around it. Like Galileo with Copernicus, Newton 
sought to generalize these principles to explain, 
not only how the planets moved, but also why 
they did. 

Almost everyone has heard the story of 
Newton and the apple — specifically, that while he 
was sitting under an apple tree, a falling apple 
struck him on the head, spurring in him a great 
intuitive leap that led him to form his theory of 
gravitation. One contemporary biographer, 
William Stukely, wrote that he and Newton were 
sitting in a garden under some apple trees when 
Newton told him that “...he was just in the same 
situation, as when formerly, the notion of gravi- 
tation came into his mind. It was occasion’d by 
the fall of an apple, as he sat in a contemplative 
mood. Why should that apple always descend 
perpendicularly to the ground, he thought to 
himself. Why should it not go sideways or 
upwards, but constantly to the earth’s centre?” 

The tale of Newton and the apple has 
become a celebrated myth, rather like that of 
George Washington and the cherry tree. It is an 
embellishment of actual events: Newton never 
said that an apple hit him on the head, just that 
he was thinking about the way that apples fell. Yet 
the story has become symbolic of the creative 
intellectual process that occurs when a thinker 
makes a vast intuitive leap in a matter of 
moments. Of course, Newton had spent many 
years contemplating these ideas, and their devel- 
opment required great effort. What is important 
is that he brought together the best work of his 
predecessors, yet transcended all that had gone 
before — and in the process, forged a model that 
explained a great deal about how the universe 
functions. 

The result was his Philosophiae Naturalis 
Principia Mathematica, or “Mathematical Princi- 
ples of Natural Philosophy.” Published in 1687, 
the book — usually referred to simply as the Prin- 
cipia — was one of the most influential works ever 
written. In it, Newton presented his three laws of 
motion, as well as his law of universal gravita- 
tion. 

The latter stated that every object in the uni- 
verse attracts every other one with a force pro- 
portional to the masses of each, and inversely 
proportional to the square of the distance 
between them. This statement requires some 
clarification with regard to its particulars, after 

VDLUME 2: REAL-LIFE PHYSICS 


which it will be reintroduced as a mathematical 
formula. 

mass and force. The three laws 
of motion are a subject unto themselves, covered 
elsewhere in this volume. However, in order to 
understand gravitation, it is necessary to under- 
stand at least a few rudimentary concepts relating 
to them. The first law identifies inertia as the ten- 
dency of an object in motion to remain in 
motion, and of an object at rest to remain at rest. 
Inertia is measured by mass, which — as the sec- 
ond law states — is a component of force. 

Specifically, the second law of motion states 
that force is equal to mass multiplied by acceler- 
ation. This means that there is an inverse rela- 
tionship between mass and acceleration: if force 
remains constant and one of these factors 
increases, the other must decrease — a situation 
that will be discussed in some depth below. 

Also, as a result of Newton’s second law, it is 
possible to define weight scientifically. People 
typically assume that mass and weight are the 
same, and indeed they are on Earth — or at least, 
they are close enough to be treated as compara- 
ble factors. Thus, tables of weights and measures 
show that a kilogram, the metric unit of mass, is 
equal to 2.2 pounds, the latter being the principal 
unit of weight in the British system. 

In fact, this is — if not a case of comparing to 
apples to oranges — certainly an instance of com- 
paring apples to apple pies. In this instance, the 
kilogram is the “apple” (a fitting Newtonian 
metaphor!) and the pound the “apple pie.” Just as 
an apple pie contains apples, but other things as 
well, the pound as a unit of force contains an 
additional factor, acceleration, not included in 
the kilo. 

British vs. si units. Physi- 
cists universally prefer the metric system, which 
is known in the scientific community as SI (an 
abbreviation of the French Systeme International 
d’Unites — that is, “International System of 
Units”). Not only is SI much more convenient to 
use, due to the fact that it is based on units of 10; 
but in discussing gravitation, the unequal rela- 
tionship between kilograms and pounds makes 
conversion to British units a tedious and ulti- 
mately useless task. 

Though Americans prefer the British system 
to SI, and are much more familiar with pounds 
than with kilos, the British unit of mass — called 
the slug — is hardly a household word. By con- 

SCIENCE DF EVERYDAY THINGS 


trast, scientists make regular use of the SI unit of 
force — named, appropriately enough, the new- 
ton. In the metric system, a newton (N) is the 
amount of force required to accelerate 1 kilo- 
gram of mass by 1 meter per second squared 
(m/s 2 ) Due to the simplicity of using SI over the 
British system, certain aspects of the discussion 
below will be presented purely in terms of SI. 
Where appropriate, however, conversion to 
British units will be offered. 

CALCULATING GRAVITATION- 
AL force. The law of universal gravitation 
can be stated as a formula for calculating the 
gravitational attraction between two objects of a 
certain mass, m 1 AND M 2 : F grav = G • 

R 2 . F grav is gravitational force, and r 2 the square of 
the distance between m l and m 2 . 

As for G, in Newton’s time the value of this 
number was unknown. Newton was aware sim- 
ply that it represented a very small quantity: 
without it, (»z 1 m 2 )/r 2 could be quite sizeable for 
objects of relatively great mass separated by a rel- 
atively small distance. When multiplied by this 
very small number, however, the gravitational 
attraction would be revealed to be very small as 
well. Only in 1798, more than a century after 
Newton’s writing, did English physicist Henry 
Cavendish (1731-1810) calculate the value of G. 

As to how Cavendish derived the figure, that 
is an exceedingly complex subject far beyond the 
scope of the present discussion. Even to identify 
G as a number is a challenging task. First of all, it 
is a unit of force multiplied by squared area, then 
divided by squared mass: in other words, it is 
expressed in terms of (N • m 2 )/kg 2 , where N 
stands for newtons, m for meters, and kg for kilo- 
grams. Nor is the coefficient, or numerical value, 
of G a whole number such as 1. A figure as large 
as 1, in fact, is astronomically huge compared to 
G, whose coefficient is 6.67 • 10 11 — in other 
words, 0.0000000000667. 

REAL-LIFE 
A P P L I C AT I □ N S 

Weight vs. Mass 

Before discussing the significance of the gravita- 
tional constant, however, at this point it is appro- 
priate to address a few issues that were raised ear- 
lier — issues involving mass and weight. In many 
ways, understanding these properties from the 


framework of physics requires setting aside 
everyday notions. 

First of all, why the distinction between 
weight and mass? People are so accustomed to 
converting pounds to kilos on Earth that the dif- 
ference is difficult to comprehend, but if one 
considers the relation of mass and weight in 
outer space, the distinction becomes much clear- 
er. Mass is the same throughout the universe, 
making it a much more fundamental characteris- 
tic — and hence, physicists typically speak in 
terms of mass rather than weight. 

Weight, on the other hand, differs according 
to the gravitational pull of the nearest large body. 
On Earth, a person weighs a certain amount, but 
on the Moon, this weight is much less, because 
the Moon possesses less mass than Earth. There- 
fore, in accordance with Newton’s formula for 
universal gravitation, it exerts less gravitational 
pull. By contrast, if one were on Jupiter, it would 
be almost impossible even to stand up, because 
the pull of gravity on that planet — with its 
greater mass — would be vastly greater than on 
Earth. 

It should be noted that mass is not at all a 
function of size: Jupiter does have a greater mass 
than Earth, but not because it is bigger. Mass, as 
noted eariier, is purely a measure of inertia: the 
more resistant an object is to a change in its 
velocity, the greater its mass. This in itself yields 
some results that seem difficult to understand as 
long as one remains wedded to the concept — 
true enough on Earth — that weight and mass are 
identical. 

A person might weigh less on the Moon, but 
it would be just as difficult to move that person 
from a resting position as it would be to do so on 
Earth. This is because the person’s mass, and 
hence his or her resistance to inertia, has not 
changed. Again, this is a mentally challenging 
concept: is not lifting a person, which implies 
upward acceleration, not an attempt to counter- 
act their inertia when standing still? Does it not 
follow that their mass has changed? Understand- 
ing the distinction requires a greater clarification 
of the relationship between mass, gravity, and 
weight. 

f = m a . Newton’s second law of motion, 
stated earlier, shows that force is equal to mass 
multiplied by acceleration, or in shorthand form, 
F = rna. To reiterate a point already made, if one 
assumes that force is constant, then mass and 


Gravity and 
Gravitation 


SCIENCE OF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


73 


Gravity and 
Gravitation 


74 


acceleration must have an inverse relationship. 
This can be illustrated by performing a simple 
experiment. 

Suppose one were to apply a certain amount 
of force to an empty shopping cart. Assuming the 
floor had just enough friction to allow move- 
ment, it would be easy for almost anyone to 
accelerate the shopping cart. Now assume that 
the shopping cart were filled with heavy lead 
balls, so that it weighed, say, 1,102 lb (500 kg). If 
one applied the same force, it would not move. 

What has changed, clearly, is the mass of the 
shopping cart. Because force remained constant, 
the rate of acceleration would become very 
small — in this case, almost infinitesimal. In the 
first case, with an empty shopping cart, the mass 
was relatively small, so acceleration was relatively 
high. 

Now to return to the subject of lifting some- 
one on the Moon. It is true that in order to lift 
that person, one would have to overcome inertia, 
and, in that sense, it would be as difficult as it is 
on Earth. But the other component of force, 
acceleration, has diminished greatly. 

Weight is, again, a unit of force, but in calcu- 
lating weight it is useful to make a slight change 
to the formula F = ma. By definition, the acceler- 
ation factor in weight is the downward accelera- 
tion due to gravity, usually rendered as g. So one’s 
weight is equal to mg — but on the Moon, g is 
much smaller than it is on Earth, and hence, the 
same amount of force yields much greater 
results. 

These facts shed new light on a question that 
bedeviled physicists at least from the time of 
Aristotle, until Galileo began clarifying the issue 
some 2,000 years later: why shouldn’t an object of 
greater mass fall at a different rate than one of 
smaller mass? There are two answers to that 
question, one general and one specific. The gen- 
eral answer — that Earth exerts more gravitation- 
al pull on an object of greater mass — requires a 
deeper examination of Newton’s gravitational 
formula. But the more specific answer, relating 
purely to conditions on Earth, is easily addressed 
by considering the effect of air resistance. 

Gravity and Air Resistance 

One of Galileo’s many achievements lay in using 
an idealized model of reality, one that does not 
take into account the many complex factors that 
affect the behavior of objects in the real world. 

VDLUME 2: REAL-LIFE PHYSICS 


This permitted physicists to study processes that 
apparently defy common sense. For instance, in 
the real world, an apple does drop at a greater 
rate of speed than does a feather. However, in a 
vacuum, they will drop at the same rate. Since 
Galileo’s time, it has become commonplace for 
physicists to discuss specific processes such as 
gravity with the assumption that all non-perti- 
nent factors (in this case, air resistance or fric- 
tion) are nonexistent or irrelevant. This greatly 
simplified the means of testing hypotheses. 

Idealization of reality makes it possible to set 
aside the things people think they know about 
the real world, where events are complicated due 
to friction. The latter may be defined as a force 
that resists motion when the surface of one 
object comes into contact with the surface of 
another. If two balls are released in an environ- 
ment free from friction — one of them simply 
dropped while the other is rolled down a curved 
surface or inclined plane — they will reach the 
bottom at the same time. This seems to go 
against everything that is known, but that is only 
because what people “know” is complicated by 
variables that have nothing to do with gravity. 

The same is true for the behavior of falling 
objects with regard to air resistance. If air resist- 
ance were not a factor, one could fire a cannon- 
ball over horizontal space and then, when the ball 
reached the highest point in its trajectory, release 
another ball from the same height — and again, 
they would hit the ground at the same time. This 
is the case, even though the cannonball that was 
fired from the cannon has to cover a great deal of 
horizontal space, whereas the dropped ball does 
not. The fact is that the rate of acceleration due 
to gravity will be identical for the two balls, and 
the fact that the ball fired from a cannon also 
covers a horizontal distance during that same 
period is irrelevant. 

terminal velgcity. In the real 
world, air resistance creates a powerful drag force 
on falling objects. The faster the rate of fall, the 
greater the drag force, until the air resistance 
forces a leveling in the rate of fall. At this point, 
the object is said to have reached terminal veloc- 
ity, meaning that its rate of fall will not increase 
thereafter. Galileo’s idealized model, on the other 
hand, treated objects as though they were falling 
in a vacuum — space entirely devoid of matter, 
including air. In such a situation, the rate of 
acceleration would continue to grow indefinitely. 

SCIENCE DF EVERYDAY THINGS 


By means of a graph, one can compare the 
behavior of an object falling through air with 
that of an object falling in a vacuum. If the x axis 
measures time and the y axis downward speed, 
the rate of an object falling in a vacuum describes 
a 60°-angle. In other words, the speed of its 
descent is increasing at a much faster rate than is 
the rate of time of its descent — as indeed should 
be the case, in accordance with gravitational 
acceleration. The behavior of an object falling 
through air, on the other hand, describes a curve. 
Up to a point, the object falls at the same rate as 
it would in a vacuum, but soon velocity begins to 
increase at a much slower rate than time. Eventu- 
ally, the curve levels off at the point where the 
object experiences terminal velocity. 

Air resistance and friction have been men- 
tioned separately as though they were two differ- 
ent forces, but in fact air resistance is simply a 
prominent form of friction. Hence air resistance 
exerts an upward force to counter the downward 
force of mass multiplied by gravity — that is, 
weight. Since g is a constant (32 ft or 9.8 m/sec 2 ), 
the greater the weight of the falling object, the 
longer it takes for air resistance to bring it to ter- 
minal velocity. 

A feather quickly reaches terminal velocity, 
whereas it takes much longer for a cannonball to 
do the same. As a result, a heavier object does 
take less time to fall, even from a great height, 
than does a light one — but this is only because of 
friction, and not because of “elements” seeking 
their “natural level.” Incidentally, if raindrops 
(which of course fall from a very great height) 
did not reach terminal velocity, they would cause 
serious injury by the time they hit the ground. 

Applying the Gravitational 
Formula 

Using Newton’s gravitational formula, it is rela- 
tively easy to calculate the pull of gravity between 
two objects. It is also easy to see why the attrac- 
tion is insignificant unless at least one of the 
objects has enormous mass. In addition, applica- 
tion of the formula makes it clear why G (the 
gravitational constant, as opposed to g, the rate of 
acceleration due to gravity) is such a tiny number. 

If two people each have a mass of 45.5 kg 
(100 lb) and stand 1 m (3.28 ft) apart, m 1 m 2 is 
equal to 2,070 kg (4,555 lb) and r 2 is equal to 1 
m 2 . Applied to the gravitational formula, this fig- 
ure is rendered as 2,070 kg 2 /l m 2 . This number is 


then multiplied by gravitational constant, which 
again is equal to 6.67 • 10 11 (N • m 2 )/kg 2 . The 
result is a net gravitational force of 0.000000138 
N (0.00000003 lb) — about the weight of a single- 
cell organism! 

earth, gravity, and weight. 

Though it is certainly interesting to calculate the 
gravitational force between any two people, com- 
putations of gravity are only significant for 
objects of truly great mass. For instance, there is 
the Earth, which has a mass of 5.98 • 10 24 kg — 
that is, 5.98 septillion (1 followed by 24 zeroes) 
kilograms. And, of course, Earth’s mass is rela- 
tively minor compared to that of several planets, 
not to mention the Sun. Yet Earth exerts enough 
gravitational pull to keep everything on it — liv- 
ing creatures, manmade structures, mountains 
and other natural features — stable and in place. 

One can calculate Earth’s gravitational force 
on any one person — if one wants to take the time 
to do so using Newton’s formula. In fact, it is 
much simpler than that: gravitational force is 
equal to weight, or m • g. Thus if a woman weighs 
100 lb (445 N), this amount is also equal to the 
gravitational force exerted on her. By divid- 
ing 445 N by the acceleration of gravity — 9.8 
m/sec 2 — it is easy to obtain her mass: 45.4 kg. 

The use of the mg formula for gravitation 
helps, once again, to explain why heavier objects 
do not fall faster than lighter ones. The figure for 
g is a constant, but for the sake of argument, let 
us assume that it actually becomes larger for 
objects with a greater mass. This in turn would 
mean that the gravitational force, or weight, 
would be bigger than it is — thus creating an 
irreconcilable logic loop. 

Furthermore, one can compare results of 
two gravitation equations, one measuring the 
gravitational force between Earth and a large 
stone, the other measuring the force between 
Earth and a small stone. (The distance between 
Earth and each stone is assumed to be the same.) 
The result will yield a higher quantity for the 
force exerted on the larger stone — but only 
because its mass is greater. Clearly, then, the 
increase of force results only from an increase in 
mass, not acceleration. 

Gravity and Curved Space 

As should be clear from Newton’s gravitational 
formula, the force of gravity works both ways: 
not only does a stone fall toward Earth, but Earth 


Gravity and 
Gravitation 


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VDLUME 2: REAL-LIFE PHYSICS 


75 


Gravity and 
Gravitation 


KEY TERMS 


force: The product of mass multi- 

plied by acceleration. 

frictidn: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

i n e rti a: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

inverse relationship: A situa- 

tion involving two variables, in which one 
of the two increases in direct proportion to 
the decrease in the other. 

LAW OF UNIVERSAL GRAVITATION: 

A principle, put forth by Sir Isaac Newton 
( 1642-1727), which states that every object 
in the universe attracts every other one 
with a force proportional to the masses of 


each, and inversely proportional to the 
square of the distance between them. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion. 

TERMINAL VELOCITY: A term 

describing the rate of fall for an object 
experiencing the drag force of air resist- 
ance. In a vacuum, the object would con- 
tinue to accelerate with the force of gravity, 
but in most real-world situations, air 
resistance creates a powerful drag force 
that causes a leveling in the object’s rate of 
fall. 

vacuum: Space entirely devoid of 

matter, including air. 

weight: A measure of the gravitational 

force on an object; the product of mass mul- 
tiplied by the acceleration due to gravity. 


76 


actually falls toward it. The mass of Earth is so 
great compared to that of the stone that the 
movement of Earth is imperceptible — but it does 
happen. Furthermore, because Earth is round, 
when one hurls a projectile at a great distance, 
Earth curves away from the projectile; but even- 
tually gravity itself forces the projectile to the 
ground. 

However, if one were to fire a rocket at 
17,700 MPH (28,500 km/h), at every instant of 
time the projectile is falling toward Earth with 
the force of gravity — but the curved Earth would 
be falling away from it at the same moment as 
well. Hence, the projectile would remain in con- 
stant motion around the planet — that is, it would 
be in orbit. 

The same is true of an artificial satellite’s 
orbit around Earth: even as the satellite falls 
toward Earth, Earth falls away from it. This same 
relationship exists between Earth and its great 
natural satellite, the Moon. Likewise, with the 

vglume z: real-life physics 


Sun and its many satellites, including Earth: 
Earth plunges toward the Sun with every instant 
of its movement, but at every instant, the Sun 
falls away. 

why is earth round? Note 
that in the above discussion, it was assumed that 
Earth and the Sun are round. Everyone knows 
that to be the case, but why? The answer is 
“Because they have to be” — that is, gravity will 
not allow them to be otherwise. In fact, the larg- 
er the mass of an object, the greater its tendency 
toward roundness: specifically, the gravitational 
pull of its interior forces the surface to assume a 
relatively uniform shape. There is a relatively 
small vertical differential for Earth’s surface: 
between the lowest point and the highest point is 
just 12.28 mi (19.6 km) — not a great distance, 
considering that Earth’s radius is about 4,000 mi 
(6,400 km). 

It is true that Earth bulges near the equator, 
but this is only because it is spinning rapidly on 

SCIENCE DF EVERYDAY THINGS 



its axis, and thus responding to the centripetal 
force of its motion, which produces a centrifugal 
component. If Earth were standing still, it would 
be much nearer to the shape of a sphere. On the 
other hand, an object of less mass is more likely 
to retain a shape that is far less than spherical. 
This can be shown by reference to the Martian 
moons Phobos and Deimos, both of which are 
oblong — and both of which are tiny, in terms of 
size and mass, compared to Earth’s Moon. 

Mars itself has a radius half that of Earth, yet 
its mass is only about 10% of Earth’s. In light of 
what has been said about mass, shape, and grav- 
ity, it should not surprising to learn that Mars is 
also home to the tallest mountain in the solar 
system. Standing 15 mi (24 km) high, the volcano 
Olympus Mons is not only much taller than 
Earth’s tallest peak, Mount Everest (29,028 ft 
[8,848 m] ); it is 22% taller than the distance from 
the top of Mount Everest to the lowest spot on 
Earth, the Mariana Trench in the Pacific Ocean 
(-35,797 ft [-10,911 m]) 

A spherical object behaves with regard to 
gravitation as though its mass were concentrated 
near its center. And indeed, 33% of Earth’s mass 
is at is core (as opposed to the crust or mantle), 
even though the core accounts for only about 
20% of the planet’s volume. Geologists believe 
that the composition of Earth’s core must be 
molten iron, which creates the planet’s vast elec- 
tromagnetic field. 

THE FRONTIERS GF GRAVITY. 

The subject of curvature with regard to gravity 
can be both a threshold or — as it is here — a point 
of closure. Investigating questions over perceived 
anomalies in Newton’s description of the behav- 
ior of large objects in space led Einstein to his 
General Theory of Relativity, which posited a 
curved four-dimensional space-time. This led to 
entirely new notions concerning gravity, mass, 
and light. But relativity, as well as its relation to 
gravity, is another subject entirely. Einstein 
offered a new understanding of gravity, and 
indeed of physics itself, that has changed the way 


thinkers both inside and outside the sciences per- 
ceive the universe. Here on Earth, however, grav- 
ity behaves much as Newton described it more 
than three centuries ago. 

Meanwhile, research in gravity continues to 
expand, as a visit to the Web site <www.Gravi- 
ty.org> reveals. Spurred by studies in relativity, a 
branch of science called relativistic astrophysics 
has developed as a synthesis of astronomy and 
physics that incorporates ideas put forth by Ein- 
stein and others. The <www.Gravity.org> site 
presents studies — most of them too abstruse for 
a reader who is not a professional scientist — 
across a broad spectrum of disciplines. Among 
these is bioscience, a realm in which researchers 
are investigating the biological effects — such as 
mineral loss and motion sickness — of exposure 
to low gravity. The results of such studies will 
ultimately protect the health of the astronauts 
who participate in future missions to outer space. 

WHERE TD LEARN MORE 

Ardley, Neil. The Science Book of Gravity. San Diego, CA: 
Harcourt Brace Jovanovich, 1992. 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Bendick, Jeanne. Motion and Gravity. New York: F. Watts, 
1972. 

Dalton, Cindy Devine. Gravity. Vero Beach, FL: Rourke, 
2001. 

David, Leonard. “Artificial Gravity and Space Travel.” Bio- 
Science, March 1992, pp. 155-159. 

Exploring Gravity — Curtin University, Australia (Web 
site), <http://www.curtin.edu.au/curtin/dept/phys- 
sci/gravity/> (March 18, 2001). 

The Gravity Society (Web site), <http://www.gravity.org> 
(March 18, 2001). 

Nardo, Don. Gravity: The Universal Force. San Diego, 

CA: Lucent Books, 1990. 

Rutherford, F. James; Gerald Holton; and Fletcher G. 
Watson. Project Physics. New York: Holt, Rinehart, 
and Winston, 1981. 

Stringer, John. The Science of Gravity. Austin, TX: Rain- 
tree Steck- Vaughn, 2000. 


GRAVITY AND 
GRAVITATION 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


77 


PROJECTILE MOTION 



C □ N C E PT 

A projectile is any object that has been thrown, 
shot, or launched, and ballistics is the study of 
projectile motion. Examples of projectiles range 
from a golf ball in flight, to a curve ball thrown 
by a baseball pitcher to a rocket fired into space. 
The flight paths of all projectiles are affected by 
two factors: gravity and, on Earth at least, air 
resistance. 

H □ W IT WDRKS 

The effects of air resistance on the behavior of 
projectiles can be quite complex. Because effects 
due to gravity are much simpler and easier to 
analyze, and since gravity applies in more situa- 
tions, we will discuss its role in projectile motion 
first. In most instances on Earth, of course, a pro- 
jectile will be subject to both forces, but there 
may be specific cases in which an artificial vacu- 
um has been created, which means it will only be 
subjected to the force of gravity. Furthermore, in 
outer space, gravity — whether from Earth or 
another body — is likely to be a factor, whereas air 
resistance (unless or until astronomers find 
another planet with air) will not be. 

The acceleration due to gravity is 32 ft 
(9.8 m)/sec 2 , usually expressed as “per second 
squared.” This means that as every second passes, 
the speed of a falling object is increasing by 
32 ft/sec (9.8 m). Where there is no air resistance, 
a ball will drop at a velocity of 32 feet per second 
after one second, 64 ft (19.5 m) per second after 
two seconds, 96 ft (29.4 m) per second after three 
seconds, and so on. When an object experiences 
the ordinary acceleration due to gravity, this fig- 
ure is rendered in shorthand as g. Actually, the 
figure of 32 ft (9.8 m) per second squared applies 

VOLUME 2: REAL-LIFE PHYSICS 


at sea level, but since the value of g changes little 
with altitude — it only decreases by 5% at a height 
of 10 mi (16 km) — it is safe to use this number. 

When a plane goes into a high-speed turn, it 
experiences much higher apparent g. This can be 
as high as 9 g, which is almost more than the 
human body can endure. Incidentally, people call 
these “g-forces,” but in fact g is not a measure of 
force but of a single component, acceleration. On 
the other hand, since force is the product of mass 
multiplied by acceleration, and since an aircraft 
subject to a high g factor clearly experiences a 
heavy increase in net force, in that sense, the 
expression “g-force” is not altogether inaccurate. 

In a vacuum, where air resistance plays no 
part, the effects of g are clearly demonstrated. 
Hence a cannonball and a feather, dropped into a 
vacuum at the same moment, would fall at exact- 
ly the same rate and hit bottom at the same time. 

The Cannonball or the 
Feather? Air Resistance vs. 
Mass 

Naturally, air resistance changes the terms of the 
above equation. As everyone knows, under ordi- 
nary conditions, a cannonball falls much faster 
than a feather, not simply because the feather is 
lighter than the cannonball, but because the air 
resists it much better. The speed of descent is a 
function of air resistance rather than mass, which 
can be proved with the following experiment. 
Using two identical pieces of paper — meaning 
that their mass is exactly the same — wad one up 
while keeping the other flat. Then drop them. 
Which one lands first? The wadded piece will fall 
faster and land first, precisely because it is less 
air-resistant than the sail-like flat piece. 

SCIENCE □ F EVERYDAY THINGS 




Because of their design, the bullets in this .357 magnum will come gut of the gun spinning, which 
greatly increases their accuracy. (Photograph by Tim Wright/Corbis. Reproduced by permission.) 


Now to analyze the motion of a projectile in 
a situation without air resistance. Projectile 
motion follows the flight path of a parabola, a 
curve generated by a point moving such that its 
distance from a fixed point on one axis is equal to 
its distance from a fixed line on the other axis. In 
other words, there is a proportional relationship 
between x and y throughout the trajectory or 
path of a projectile in motion. Most often this 
parabola can be visualized as a simple up-and- 
down curve like the shape of a domed roof. (The 
Gateway Arch in St. Louis, Missouri, is a steep 
parabola.) 

Instead of referring to the more abstract val- 
ues of x and y, we will separate projectile motion 
into horizontal and vertical components. Gravity 
plays a role only in vertical motion, whereas 
obviously, horizontal motion is not subject to 
gravitational force. This means that in the 
absence of air resistance, the horizontal velocity 
of a projectile does not change during flight; by 
contrast, the force of gravity will ultimately 
reduce its vertical velocity to zero, and this will in 
turn bring a corresponding drop in its horizontal 
velocity. 

In the case of a cannonball fired at a 45° 
angle — the angle of maximum efficiency for 
height and range together — gravity will eventu- 

SCIENCE □ E EVERYDAY THINGS 


ally force the projectile downward, and once it 
hits the ground, it can no longer continue on its 
horizontal trajectory. Not, at least, at the same 
velocity: if you were to thrust a bowling ball for- 
ward, throwing it with both hands from the solar 
plexus, its horizontal velocity would be reduced 
greatly once gravity forced it to the floor. 
Nonetheless, the force on the ball would proba- 
bly be enough (assuming the friction on the floor 
was not enormous) to keep the ball moving in a 
horizontal direction for at least a few more feet. 

There are several interesting things about 
the relationship between gravity and horizontal 
velocity. Assuming, once again, that air resistance 
is not a factor, the vertical acceleration of a pro- 
jectile is g. This means that when a cannonball is 
at the highest point of its trajectory, you could 
simply drop another cannonball from exactly the 
same height, and they would land at the same 
moment. This seems counterintuitive, or oppo- 
site to common sense: after all, the cannonball 
that was fired from the cannon has to cover a 
great deal of horizontal space, whereas the 
dropped ball does not. Nonetheless, the rate of 
acceleration due to gravity will be identical for 
the two balls, and the fact that the ball fired from 
a cannon also covers a horizontal distance during 
that same period is purely incidental. 

VDLUME 2: REAL-LIFE PHYSICS 


79 



PRDJECTILE 

Motion 


B □ 


Gravity, combined with the first law of 
motion, also makes it possible (in theory at least) 
for a projectile to keep moving indefinitely. This 
actually does take place at high altitudes, when a 
satellite is launched into orbit: Earth’s gravita- 
tional pull, combined with the absence of air 
resistance or other friction, ensures that the satel- 
lite will remain in constant circular motion 
around the planet. The same is theoretically pos- 
sible with a cannonball at very low altitudes: if 
one could fire a ball at 17,700 MPH (28,500 
k/mh), the horizontal velocity would be great 
enough to put the ball into low orbit around 
Earth’s surface. 

The addition of air resistance or airflow to 
the analysis of projectile motion creates a num- 
ber of complications, including drag, or the force 
that opposes the forward motion of an object in 
airflow. Typically, air resistance can create a drag 
force proportional to the squared value of a pro- 
jectile’s velocity, and this will cause it to fall far 
short of its theoretical range. 

Shape, as noted in the earlier illustration 
concerning two pieces of paper, also affects air 
resistance, as does spin. Due to a principle known 
as the conservation of angular momentum, an 
object that is spinning tends to keep spinning; 
moreover, the orientation of the spin axis (the 
imaginary “pole” around which the object is 
spinning) tends to remain constant. Thus spin 
ensures a more stable flight. 

REAL-LIFE 
A P P L I C AT IONS 

Bullets on a Straight 
Spinning Flight 

One of the first things people think of when they 
hear the word “ballistics” is the study of gunfire 
patterns for the purposes of crime-solving. 
Indeed, this application of ballistics is a signifi- 
cant part of police science, because it allows law- 
enforcement investigators to determine when, 
where, and how a firearm was used. In a larger 
sense, however, the term as applied to firearms 
refers to efforts toward creating a more effective, 
predictable, and longer bullet trajectory. 

From the advent of firearms in the West dur- 
ing the fourteenth century until about 1500, 
muskets were hopelessly unreliable. This was 
because the lead balls they fired had not been fit- 

VDLUME 2: REAL-LIFE PHYSICS 


ted to the barrel of the musket. When fired, they 
bounced erratically off the sides of the barrel, 
and this made their trajectories unpredictable. 
Compounding this was the unevenness of the 
lead balls themselves, and this irregularity of 
shape could lead to even greater irregularities in 
trajectory. 

Around 1500, however, the first true rifles 
appeared, and these greatly enhanced the accura- 
cy of firearms. The term rifle comes from the 
“rifling” of the musket barrels: that is, the barrels 
themselves were engraved with grooves, a process 
known as rifling. Furthermore, ammunition- 
makers worked to improve the production 
process where the musket balls were concerned, 
producing lead rounds that were more uniform 
in shape and size. 

Despite these improvements, soldiers over 
the next three centuries still faced many chal- 
lenges when firing lead balls from rifled barrels. 
The lead balls themselves, because they were 
made of a soft material, tended to become mis- 
shapen during the loading process. Furthermore, 
the gunpowder that propelled the lead balls had 
a tendency to clog the rifle barrel. Most impor- 
tant of all was the fact that these rifles took time 
to load — and in a situation of battle, this could 
cost a man his life. 

The first significant change came in the 
1840s, when in place of lead balls, armies began 
using bullets. The difference in shape greatly 
improved the response of rounds to aerodynam- 
ic factors. In 1847, Claude-Etienne Minie, a cap- 
tain in the French army, developed a bullet made 
of lead, but with a base that was slightly hollow. 
Thus when fired, the lead in the round tended to 
expand, filling the barrel’s diameter and gripping 
the rifling. 

As a result, the round came out of the barrel 
end spinning, and continued to spin throughout 
its flight. Not only were soldiers able to fire their 
rifles with much greater accuracy, but thanks to 
the development of chambers and magazines, 
they could reload more quickly. 

Curve Balls, Dimpled Gglf 
Balls, and Other Tricks with 
Spin 

In the case of a bullet, spin increases accuracy, 
ensuring that the trajectory will follow an expect- 
ed path. But sometimes spin can be used in more 

science of everyday things 


complex ways, as with a curveball thrown by a 
baseball pitcher. 

The invention of the curveball is credited to 
Arthur “Candy” Cummings, who as a pitcher for 
the Brooklyn Excelsiors at the age of 18 in 1867 — 
an era when baseball was still very young — intro- 
duced a new throw he had spent several years 
perfecting. Snapping as he released the ball, he 
and the spectators (not to mention the startled 
batter for the opposing team) watched as the 
pitch arced, then sailed right past the batter for a 
strike. 

The curveball bedeviled baseball players and 
fans alike for many years thereafter, and many 
dismissed it as a type of optical illusion. The 
debate became so heated that in 1941, both Life 
and Look magazines ran features using stop- 
action photography to show that a curveball 
truly did curve. Even in 1982, a team of 
researchers from General Motors (CM) and the 
Massachusetts Institute of Technology (MIT), 
working at the behest of Science magazine, inves- 
tigated the curveball to determine if it was more 
than a mere trick. 

In fact, the curveball is a trick, but there is 
nothing fake about it. As the pitcher releases the 
ball, he snaps his wrist. This puts a spin on the 
projectile, and air resistance does the rest. As the 
ball moves toward the plate, its spin moves 
against the air, which creates an airstream mov- 
ing against the trajectory of the ball itself. The 
airstream splits into two lines, one curving over 
the ball and one curving under, as the ball sails 
toward home plate. 

For the purposes of clarity, assume that you 
are viewing the throw from a position between 
third base and home. Thus, the ball is moving 
from left to right, and therefore the direction of 
airflow is from right to left. Meanwhile the ball, 
as it moves into the airflow, is spinning clock- 
wise. This means that the air flowing over the top 
of the ball is moving in a direction opposite to 
the spin, whereas that flowing under it is moving 
in the same direction as the spin. 

This creates an interesting situation, thanks 
to Bernoulli’s principle. The latter, formulated by 
Swiss mathematician and physicist Daniel 
Bernoulli (1700-1782), holds that where velocity 
is high, pressure is low — and vice versa. Bernoul- 
li’s principle is of the utmost importance to aero- 
dynamics, and likewise plays a significant role in 
the operation of a curveball. At the top of the 

SCIENCE □ E EVERYDAY THINGS 


i 

t 1 






Golf balls are dimpled because they travel much 
farther than nqndimpled ONES. (Photograph by D. 
Boone/Corbis. Reproduced by permission.) 

ball, its clockwise spin is moving in a direction 
opposite to the airflow. This produces drag, slow- 
ing the ball, increasing pressure, and thus forcing 
it downward. At the bottom end of the ball, how- 
ever, the clockwise motion is flowing with the air, 
thus resulting in higher velocity and lower pres- 
sure. As per Bernoulli’s principle, this tends to 
pull the ball downward. 

In the 60-ft, 6-in (18.4-m) distance that sep- 
arates the pitcher’s mound from home plate on a 
regulation major-league baseball field, a curve- 
ball can move downward by a foot (0.3048 m) or 
more. The interesting thing here is that this 
downward force is almost entirely due to air 
resistance rather than gravity, though of course 
gravity eventually brings any pitch to the ground, 
assuming it has not already been hit, caught, or 
bounced off a fence. 

A curveball represents a case in which spin is 
used to deceive the batter, but it is just as possible 
that a pitcher may create havoc at home plate by 
throwing a ball with little or no spin. This is 
called a knuckleball, and it is based on the fact 
that spin in general — though certainly not the 
deliberate spin of a curveball — tends to ensure a 

VDLUME 2: REAL-LIFE PHYSICS 


PROJECTILE 

MOTION 


B 1 



PRDJECTILE 

Motion 


BZ 


more regular trajectory. Because a knuckleball 
has no spin, it follows an apparently random 
path, and thus it can be every bit as tricky for the 
pitcher as for the batter. 

Golf, by contrast, is a sport in which spin is 
expected: from the moment a golfer hits the ball, 
it spins backward — and this in turn helps to 
explain why golf balls are dimpled. Early golf 
balls, known as featheries, were merely smooth 
leather pouches containing goose feathers. The 
smooth surface seemed to produce relatively low 
drag, and golfers were impressed that a well-hit 
feathery could travel 150-175 yd (137-160 m). 

Then in the late nineteenth century, a pro- 
fessor at St. Andrews University in Scotland real- 
ized that a scored or marked ball would travel 
farther than a smooth one. (The part about St. 
Andrews may simply be golfing legend, since the 
course there is regarded as the birthplace of golf 
in the fifteenth century.) Whatever the case, it is 
true that a scored ball has a longer trajectory, 
again as a result of the effect of air resistance on 
projectile motion. 

Airflow produces two varieties of drag on a 
sphere such as a golf ball: drag due to friction, 
which is only a small aspect of the total drag, and 
the much more significant drag that results from 
the separation of airflow around the ball. As with 
the curveball discussed earlier, air flows above 
and below the ball, but the issue here is more 
complicated than for the curved pitch. 

Airflow comes in two basic varieties: lami- 
nar, meaning streamlined; or turbulent, indicat- 
ing an erratic, unpredictable flow. For a jet flying 
through the air, it is most desirable to create a 
laminar flow passing over its airfoil, or the 
curved front surface of the wing. In the case of 
the golf ball, however, turbulent flow is more 
desirable. 

In laminar flow, the airflow separates quick- 
ly, part of it passing over the ball and part passing 
under. In turbulent flow, however, separation 
comes later, further back on the ball. Each form 
of air separation produces a separation region, an 
area of drag that the ball pulls behind it (so to 
speak) as it flies through space. But because the 
separation comes further back on the ball in tur- 
bulent flow, the separation region itself is nar- 
rower, thus producing less drag. 

Clearly, scoring the ball produced turbulent 
flow, and for a few years in the early twentieth 
century, manufacturers experimented with 

VDLUME 2: REAL-LIFE PHYSICS 


designs that included squares, rectangles, and 
hexagons. In time, they settled on the dimpled 
design known today. Golf balls made in Britain 
have 330 dimples, and those in America 336; in 
either case, the typical drive distance is much, 
much further than for an unscored ball — 180- 
250 yd (165-229 m). 

Powered Projectiles: Rock- 
ets and Missiles 

The most complex form of projectile widely 
known in modern life is the rocket or missile. 
Missiles are unmanned vehicles, most often used 
in warfare to direct some form of explosive 
toward an enemy. Rockets, on the other hand, 
can be manned or unmanned, and may be 
propulsion vehicles for missiles or for spacecraft. 
The term rocket can refer either to the engine or 
to the vehicle it propels. 

The first rockets appeared in China during 
the late medieval period, and were used unsuc- 
cessfully by the Chinese against Mongol invaders 
in the early part of the thirteenth century. Euro- 
peans later adopted rocketry for battle, as for 
instance when French forces under Joan of Arc 
used crude rockets in an effort to break the siege 
on Orleans in 1429. 

Within a century or so, however, rocketry as 
a form of military technology became obsolete, 
though projectile warfare itself remained as 
effective a method as ever. From the catapults of 
Roman times to the cannons that appeared in the 
early Renaissance to the heavy artillery of today, 
armies have been shooting projectiles against 
their enemies. The crucial difference between 
these projectiles and rockets or missiles is that the 
latter varieties are self-propelled. 

Only around the end of World War II did 
rocketry and missile warfare begin to reappear in 
new, terrifying forms. Most notable among these 
was Hitler’s V-2 “rocket” (actually a missile), 
deployed against Great Britain in 1944, but for- 
tunately developed too late to make an impact. 
The 1950s saw the appearance of nuclear war- 
heads such as the ICBM (intercontinental ballis- 
tic missile). These were guided missiles, as 
opposed to the V-2, which was essentially a huge 
self-propelled bullet fired toward London. 

More effective than the ballistic missile, 
however, was the cruise missile, which appeared 
in later decades and which included aerodynam- 
ic structures that assisted in guidance and 

science of everyday things 


Projectile 

Motion 



In the case of a rocket, like this Patriot missile being launched during a test, propulsion comes by 

EXPELLING FLUID WHICH IN SCIENTIFIC TERMS CAN MEAN A GAS AS WELL AS A LIQUID FROM ITS REAR END. MOST 

OFTEN THIS FLUID IS A MASS OF HOT GASES PRODUCED BY A CHEMICAL REACTION INSIDE THE ROCKET’S BODY, AND 
THIS BACKWARD MOTION CREATES AN EQUAL AND OPPOSITE REACTION FROM THE ATMOSPHERE, PROPELLING THE 

rocket forward. (Corbis. Reproduced by permission.) 


maneuvering. In addition to guided or unguided, 
ballistic or aerodynamic, missiles can be classi- 
fied in terms of source and target: surface-to-sur- 
face, air-to-air, and so on. By the 1970s, the Unit- 
ed States had developed an extraordinarily 
sophisticated surface-to-air missile, the Stinger. 
Stingers proved a decisive factor in the Afghan- 
Soviet War (1979-89), when U.S. -supplied 
Afghan guerrillas used them against Soviet air- 
craft. 

In the period from the late 1940s to the late 
1980s, the United States, the Soviet Union, and 
other smaller nuclear powers stockpiled these 
warheads, which were most effective precisely 

SCIENCE □ F EVERYDAY THINGS 


because they were never used. Thus, U.S. Presi- 
dent Ronald Reagan played an important role in 
ending the Cold War, because his weapons 
buildup forced the Soviets to spend money they 
did not have on building their own arsenal. Dur- 
ing the aftermath of the Cold War, America and 
the newly democratized Russian Federation 
worked to reduce their nuclear stockpiles. Ironi- 
cally, this was also the period when sophisticated 
missiles such as the Patriot began gaining wide- 
spread use in the Persian Gulf War and later 
conflicts. 

Certain properties unite the many varieties 
of rocket that have existed across time and 

VDLUME 2: REAL-LIFE PHYSICS 


S 3 


PROJECTILE 

Motion 


KEY TERMS 


acceleration: A change in velocity 

over a given time period. 

aerodynamic: Relating to airflow. 

ballistics: The study of projectile 

motion. 

drag: The force that opposes the for- 

ward motion of an object in airflow. In 
most cases, its opposite is lift. 

first law of motion: A principle, 

formulated by Sir Isaac Newton (1642- 
1727), which states that an object at rest 
will remain at rest, and an object in motion 
will remain in motion, at a constant veloci- 
ty unless or until outside forces act upon it. 

friction: Any force that resists the 

motion of body in relation to another with 
which it is in contact. 

inertia: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

l a m i n a r : A term describing a stream- 
lined flow, in which all particles move at 
the same speed and in the same direction. 
Its opposite is turbulent flow. 

lift: An aerodynamic force perpendi- 

cular to the direction of the wind. In most 
cases, its opposite is drag. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. 

parabola: A curve generated by a 

point moving such that its distance from a 
fixed point on one axis is equal to its dis- 
tance from a fixed line on the other axis. As 


a result, between any two points on the 
parabola there is a proportional relation- 
ship between x and y values. 

prgjectile: Any object that has 

been thrown, shot, or launched. 

specific impulse: A measure of 

rocket fuel efficiency — specifically, the 
mass that can be lifted by a particular type 
of fuel for each pound of fuel consumer 
(that is, the rocket and its contents) per 
second of operation time. Figures for spe- 
cific impulse are rendered in seconds. 

speed: The rate at which the position 

of an object changes over a given period of 
time. Unlike velocity, direction is not a 
component of speed. 

THIRD LAW DF MOTION: A princi- 

ple, which like the first law of motion was 
formulated by Sir Isaac Newton. The third 
law states that when one object exerts a 
force on another, the second object exerts 
on the first a force equal in magnitude but 
opposite in direction. 

traj ecto ry: The path of a projectile 

in motion, a parabola upward and across 
space. 

turbulent: A term describing a 

highly irregular form of flow, in which a 
fluid is subject to continual changes in 
speed and direction. Its opposite is laminar 
flow. 

velocity: The speed of an object in a 

particular direction. 

viscgsity: The internal friction in a 

fluid that makes it resistant to flow. 


B 4 


VDLUME 2: real-life physics 


SCIENCE GF EVERYDAY THINGS 



space — including the relatively harmless fire- 
works used in Fourth of July and New Year’s Eve 
celebrations around the country. One of the key 
principles that makes rocket propulsion possible 
is the third law of motion. Sometimes colloquial- 
ly put as “For every action, there is an equal and 
opposite reaction,” a more scientifically accurate 
version of this law would be: “When one object 
exerts a force on another, the second object exerts 
on the first a force equal in magnitude but oppo- 
site in direction.” 

In the case of a rocket, propulsion comes by 
expelling fluid — which in scientific terms can 
mean a gas as well as a liquid — from its rear. 
Most often this fluid is a mass of hot gases pro- 
duced by a chemical reaction inside the rocket’s 
body, and this backward motion creates an equal 
and opposite reaction from the rocket, propelling 
it forward. 

Before it undergoes a chemical reaction, 
rocket fuel may be either in solid or liquid form 
inside the rocket’s fuel chamber, though it ends 
up as a gas when expelled. Both solid and liquid 
varieties have their advantages and disadvantages 
in terms of safety, convenience, and efficiency in 
lifting the craft. Scientists calculate efficiency by a 
number of standards, among them specific 
impulse, a measure of the mass that can be lifted 
by a particular type of fuel for each pound of fuel 
consumed (that is, the rocket and its contents) 
per second of operation time. Figures for specif- 
ic impulse are rendered in seconds. 

A spacecraft may be divided into segments 
or stages, which can be released as specific points 


along the flight in part to increase specific 
impulse. This was the case with the Saturn 5 
rockets that carried astronauts to the Moon in 
the period 1969-72, but not with the varieties of 
space shuttle that have flown regular missions 
since 1981. 

The space shuttle is essentially a hybrid of an 
airplane and rocket, with a physical structure 
more like that of an aircraft but with rocket 
power. In fact, the shuttle uses many rockets to 
maximize efficiency, utilizing no less than 67 
rockets — 49 of which run on liquid fuel and the 
rest on solid fuel — at different stages of its flight. 

WHERE TO LEARN MORE 

“Aerodynamics in Sports Equipment.” K8AIT Principles of 
Aeronautics — Advanced (Web site). 
<http://muttley.ucdavis.edu/Book/Sports/advanced/ 
index.html> (March 2, 2001). 

Asimov, Isaac. Exploring Outer Space: Rockets, Probes, and 
Satellites. Revisions and updates by Francis Reddy. 
Milwaukee, WI: G. Stevens, 1995. 

How in the World? Pleasantville, N.Y.: Reader’s Digest, 
1990. 

“Interesting Properties of Projectile of Motion” (Web site) . 
<http://www.phy.ntnu.edu.tw/~hwang/projectile3/ 
projectile3.html> (March 2, 2001). 

JBM Small Arms Ballistics (Web site). <http://roadrun- 
ner.com/~jbm/index_rgt.html> (March 2, 2001). 

The Physics of Projectile Motion (Web site). 

<http://library.thinkquest.org/2779/> (March 2, 
2001 ). 

Richardson, Hazel. How to Build a Rocket. Illustrated by 
Scoular Anderson. New York: F. Watts, 2001. 


Projectile 

Motion 


SCIENCE OF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


B5 


TORQUE 


C □ N C E PT 

Torque is the application of force where there is 
rotational motion. The most obvious example of 
torque in action is the operation of a crescent 
wrench loosening a lug nut, and a close second is 
a playground seesaw. But torque is also crucial to 
the operation of gyroscopes for navigation, and 
of various motors, both internal-combustion 
and electrical. 

H □ W IT WDRKS 

Force, which may be defined as anything that 
causes an object to move or stop moving, is the 
linchpin of the three laws of motion formulated 
by Sir Isaac Newton (1642-1727.) The first law 
states that an object at rest will remain at rest, 
and an object in motion will remain in motion, 
unless or until outside forces act upon it. The sec- 
ond law defines force as the product of mass 
multiplied by acceleration. According to the third 
law, when one object exerts a force on another, 
the second object exerts on the first a force equal 
in magnitude but opposite in direction. 

One way to envision the third law is in terms 
of an active event — for instance, two balls strik- 
ing one another. As a result of the impact, each 
flies backward. Given the fact that the force on 
each is equal, and that force is the product of 
mass and acceleration (this is usually rendered 
with the formula F = ma), it is possible to make 
some predictions regarding the properties of 
mass and acceleration in this interchange. For 
instance, if the mass of one ball is relatively small 
compared to that of the other, its acceleration 
will be correspondingly greater, and it will thus 
be thrown backward faster. 

VDLUME 2: REAL-LIFE PHYSICS 


On the other hand, the third law can be 
demonstrated when there is no apparent move- 
ment, as for instance, when a person is sitting on 
a chair, and the chair exerts an equal and oppo- 
site force upward. In such a situation, when all 
the forces acting on an object are in balance, that 
object is said to be in a state of equilibrium. 

Physicists often discuss torque within the 
context of equilibrium, even though an object 
experiencing net torque is definitely not in equi- 
librium. In fact, torque provides a convenient 
means for testing and measuring the degree of 
rotational or circular acceleration experienced by 
an object, just as other means can be used to cal- 
culate the amount of linear acceleration. In equi- 
librium, the net sum of all forces acting on an 
object should be zero; thus in order to meet the 
standards of equilibrium, the sum of all torques 
on the object should also be zero. 

REAL-LIFE 
A P P L I C AT I □ N S 

Seesaws and Wrenches 

As for what torque is and how it works, it is best 
discuss it in relationship to actual objects in the 
physical world. Two in particular are favorites 
among physicists discussing torque: a seesaw and 
a wrench turning a lug nut. Both provide an easy 
means of illustrating the two ingredients of 
torque, force and moment arm. 

In any object experiencing torque, there is a 
pivot point, which on the seesaw is the balance- 
point, and which in the wrench-and-lug nut 
combination is the lug nut itself. This is the area 
around which all the forces are directed. In each 

SCIENCE □ F EVERYDAY THINGS 



Torque 



A seesaw rotates ON and OFF the ground due to TORguE imbalance. (Photograph by Dean Conger/ Corbis. Reproduced 
by permission.) 


case, there is also a place where force is being 
applied. On the seesaw, it is the seats, each hold- 
ing a child of differing weight. In the realm of 
physics, weight is actually a variety of force. 

Whereas force is equal to mass multiplied by 
acceleration, weight is equal to mass multiplied 
by the acceleration due to gravity. The latter is 
equal to 32 ft (9.8 m)/sec 2 . This means that for 
every second that an object experiencing gravita- 
tional force continues to fall, its velocity increas- 
es at the rate of 32 ft or 9.8 m per second. Thus, 
the formula for weight is essentially the same as 
that for force, with a more specific variety of 
acceleration substituted for the generalized term 
in the equation for force. 

As for moment arm, this is the distance from 
the pivot point to the vector on which force is 
being applied. Moment arm is always perpendi- 
cular to the direction of force. Consider a wrench 
operating on a lug nut. The nut, as noted earlier, 
is the pivot point, and the moment arm is the dis- 
tance from the lug nut to the place where the per- 
son operating the wrench has applied force. The 
torque that the lug nut experiences is the product 
of moment arm multiplied by force. 

In English units, torque is measured in 
pound-feet, whereas the metric unit is Newton- 
meters, or N-m. (One newton is the amount of 

SCIENCE □ E EVERYDAY THINGS 


force that, when applied to 1 kg of mass, will give 
it an acceleration of 1 m/sec 2 ). Hence if a person 
were to a grip a wrench 9 in (23 cm) from the 
pivot point, the moment arm would be 0.75 ft 
(0.23 m.) If the person then applied 50 lb (1 1.24 
N) of force, the lug nut would be experiencing 
37.5 pound-feet (2.59 N*m) of torque. 

The greater the amount of torque, the 
greater the tendency of the object to be put into 
rotation. In the case of a seesaw, its overall design, 
in particular the fact that it sits on the ground, 
means that its board can never undergo anything 
close to 360° rotation; nonetheless, the board 
does rotate within relatively narrow parameters. 
The effects of torque can be illustrated by imag- 
ining the clockwise rotational behavior of a see- 
saw viewed from the side, with a child sitting on 
the left and a teenager on the right. 

Suppose the child weighs 50 lb (11.24 N) 
and sits 3 ft (0.91 m) from the pivot point, giving 
her side of the seesaw a torque of 150 pound-feet 
(10.28 N*m). On the other side, her teenage sister 
weighs 100 lb (22.48 N) and sits 6 ft (1.82 m) 
from the center, creating a torque of 600 pound- 
feet (40.91 N-m). As a result of the torque imbal- 
ance, the side holding the teenager will rotate 
clockwise, toward the ground, causing the child’s 
side to also rotate clockwise — off the ground. 

VDLUME 2: REAL-LIFE PHYSICS 


B7 



Torque 



Torque, along with angular momentum, is the leading factor dictating the motion of a gyroscope. 
Here, a woman rides inside a giant gyroscope at an amusement park. (Photograph by Richard Cummins/Corbis. Repro- 
duced by permission.) 


SB 


In order for the two to balance one another 
perfectly, the torque on each side has to be 
adjusted. One way would be by changing weight, 
but a more likely remedy is a change in position, 

VDLUME 2: REAL-LIFE PHYSICS 


and therefore, of moment arm. Since the teenag- 
er weighs exactly twice as much as the child, the 
moment arm on the child’s side must be exactly 
twice as long as that on the teenager’s. 

SCIENCE OF EVERYDAY THINGS 


Torque 


Hence, a remedy would be for the two to 
switch positions with regard to the pivot point. 
The child would then move out an additional 3 ft 
(.91 m), to a distance of 6 ft (1.83 m) from the 
pivot, and the teenager would cut her distance 
from the pivot point in half, to just 3 ft (.91 m). In 
fact, however, any solution that gave the child a 
moment arm twice as long as that of the teenager 
would work: hence, if the teenager sat 1 ft (.3 m) 
from the pivot point, the child should be at 2 ft (.61 
m) in order to maintain the balance, and so on. 

On the other hand, there are many situations 
in which you maybe unable to increase force, but 
can increase moment arm. Suppose you were try- 
ing to disengage a particularly stubborn lug nut, 
and after applying all your force, it still would not 
come loose. The solution would be to increase 
moment arm, either by grasping the wrench fur- 
ther from the pivot point, or by using a longer 
wrench. 

For the same reason, on a door, the knob is 
placed as far as possible from the hinges. Here the 
hinge is the pivot point, and the door itself is the 
moment arm. In some situations of torque, how- 
ever, moment arm may extend over “empty 
space,” and for this reason, the handle of a 
wrench is not exactly the same as its moment 
arm. If one applies force on the wrench at a 90°- 
angle to the handle, then indeed handle and 
moment arm are identical; however, if that force 
were at a 45° angle, then the moment arm would 
be outside the handle, because moment arm and 
force are always perpendicular. And if one were 
to pull the wrench away from the lug nut, then 
there would be 0° difference between the direc- 
tion of force and the pivot point — meaning that 
moment arm (and hence torque) would also be 
equal to zero. 

Gyroscopes 

A gyroscope consists of a wheel-like disk, called a 
flywheel, mounted on an axle, which in turn is 
mounted on a larger ring perpendicular to the 
plane of the wheel itself. An outer circle on the 
same plane as the flywheel provides structural 
stability, and indeed, the gyroscope may include 
several such concentric rings. Its focal point, 
however, is the flywheel and the axle. One end of 
the axle is typically attached to some outside 
object, while the other end is left free to float. 

Once the flywheel is set spinning, gravity has 
a tendency to pull the unattached end of the axle 

SCIENCE □ E EVERYDAY THINGS 


downward, rotating it on an axis perpendicular to 
that of the flywheel. This should cause the gyro- 
scope to fall over, but instead it begins to spin a 
third axis, a horizontal axis perpendicular both to 
the plane of the flywheel and to the direction of 
gravity. Thus, it is spinning on three axes, and as a 
result becomes very stable — that is, very resistant 
toward outside attempts to upset its balance. 

This in turn makes the gyroscope a valued 
instrument for navigation: due to its high degree 
of gyroscopic inertia, it resists changes in orienta- 
tion, and thus can guide a ship toward its destina- 
tion. Gyroscopes, rather than magnets, are often 
the key element in a compass. A magnet will point 
to magnetic north, some distance from “true 
north” (that is, the North Pole.) But with a gyro- 
scope whose axle has been aligned with true north 
before the flywheel is set spinning, it is possible to 
possess a much more accurate directional indica- 
tor. For this reason, gyroscopes are used on air- 
planes — particularly those flying over the poles — 
as well as submarines and even the Space Shuttle. 

Torque, along with angular momentum, is 
the leading factor dictating the motion of a gyro- 
scope. Think of angular momentum as the 
momentum (mass multiplied by velocity) that a 
turning object acquires. Due to a principle 
known as the conservation of angular momen- 
tum, a spinning object has a tendency to reach a 
constant level of angular momentum, and in 
order to do this, the sum of the external torques 
acting on the system must be reduced to zero. 
Thus angular momentum “wants” or “needs” to 
cancel out torque. 

The “right-hand rule” can help you to 
understand the torque in a system such as the 
gyroscope. If you extend your right hand, palm 
downward, your fingers are analogous to the 
moment arm. Now if you curl your fingers 
downward, toward the ground, then your finger- 
tips point in the direction of g — that is, gravita- 
tional force. At that point, your thumb (involun- 
tarily, due to the bone structure of the hand) 
points in the direction of the torque vector. 

When the gyroscope starts to spin, the vec- 
tors of angular momentum and torque are at 
odds with one another. Were this situation to 
persist, it would destabilize the gyroscope; 
instead, however, the two come into alignment. 
Using the right-hand rule, the torque vector on a 
gyroscope is horizontal in direction, and the vec- 
tor of angular momentum eventually aligns with 

VDLUME 2: REAL-LIFE PHYSICS 


B9 


Torque 


KEY TERMS 


acceleration: A change in veloci- 

ty over a given time period. 

equilibrium: A situation in which 

the forces acting upon an object are in 
balance. 

force: The product of mass multi- 

plied by acceleration. 

inertia: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion — including a change in velocity. 

moment arm: For an object experi- 

encing torque, moment arm is the distance 
from the pivot or balance point to the vec- 
tor on which force is being applied. 


Moment arm is always perpendicular to 
the direction of force. 

speed: The rate at which the position 

of an object changes over a given period of 
time. 

torque: The product of moment 

arm multiplied by force. 

vector: A quantity that possesses 

both magnitude and direction. By contrast, 
a scalar quantity is one that possesses only 
magnitude, with no specific direction. 

velocity: The speed of an object in a 

particular direction. 

we i g ht: A measure of the gravitation- 

al force on an object; the product of mass 
multiplied by the acceleration due to 
gravity. 


9D 


it. To achieve this, the gyroscope experiences 
what is known as gyroscopic precession, pivoting 
along its support post in an effort to bring angu- 
lar momentum into alignment with torque. Once 
this happens, there is no net torque on the sys- 
tem, and the conservation of angular momen- 
tum is in effect. 

Tdrgjue in Complex Machines 

Torque is a factor in several complex machines 
such as the electric motor that — with varia- 
tions — runs most household appliances. It is 
especially important to the operation of automo- 
biles, playing a significant role in the engine and 
transmission. 

An automobile engine produces energy, 
which the pistons or rotor convert into torque for 
transmission to the wheels. Though torque is 
greatest at high speeds, the amount of torque 
needed to operate a car does not always vary pro- 
portionately with speed. At moderate speeds and 
on level roads, the engine does not need to pro- 
vide a great deal of torque. But when the car is 
starting, or climbing a steep hill, it is important 

VDLUME z: real-life physics 


that the engine supply enough torque to keep the 
car running; otherwise it will stall. To allocate 
torque and speed appropriately, the engine may 
decrease or increase the number of revolutions 
per minute to which the rotors are subjected. 

Torque comes from the engine, but it has to 
be supplied to the transmission. In an automatic 
transmission, there are two principal compo- 
nents: the automatic gearbox and the torque con- 
verter. It is the job of the torque converter to 
transmit power from the flywheel of the engine 
to the gearbox, and it has to do so as smoothly as 
possible. The torque converter consists of three 
elements: an impeller, which is turned by the 
engine flywheel; a reactor that passes this motion 
on to a turbine; and the turbine itself, which 
turns the input shaft on the automatic gearbox. 
An infusion of oil to the converter assists the 
impeller and turbine in synchronizing move- 
ment, and this alignment of elements in the 
torque converter creates a smooth relationship 
between engine and gearbox. This also leads to 
an increase in the car’s overall torque — that is, its 
turning force. 

SCIENCE GF EVERYDAY THINGS 



Torque is also important in the operation of 
electric motors, found in everything from vacu- 
um cleaners and dishwashers to computer print- 
ers and videocassette recorders to subway sys- 
tems and water-pumping stations. Torque in the 
context of electricity involves reference to a num- 
ber of concepts beyond the scope of this discus- 
sion: current, conduction, magnetic field, and 
other topics relevant to electromagnetic force. 

WHERE T □ LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 


Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

“Rotational Motion.” Physics Department, University of 
Guelph (Web site). 

<http://www.physics.uoguelph.ca/tutorials/torque/> 
(March 4, 2001). 

“Rotational Motion — Torque.” Lee College (Web site). 
<http://www.lee.edu/mathscience/physics/physics/ 
Courses/LabManual/2b/2b.html> (March 4, 2001). 

Schweiger, Peggy E. “Torque” (Web site). 

<http://www.cyberclassrooms.net/~pschweiger/rot- 
mot.html> (March 4, 2001). 

“Torque and Rotational Motion” (Web site). 

<http://online.cctt.org/curriculumguide/units/torque 
.asp> (March 4, 2001). 


Torque 


9 1 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 

REAL-LIFE PHYSICS 

FLUID MECHANICS 

FLUID MECHANICS 
AERODYNAMICS 
BERNOULLI’S PRINCIPLE 
BUD YA N C Y 


S3 



FLUID MECHANICS 


C □ N C E PT 

The term “fluid” in everyday language typically 
refers only to liquids, but in the realm of physics, 
fluid describes any gas or liquid that conforms to 
the shape of its container. Fluid mechanics is the 
study of gases and liquids at rest and in motion. 
This area of physics is divided into fluid statics, 
the study of the behavior of stationary fluids, and 
fluid dynamics, the study of the behavior of mov- 
ing, or flowing, fluids. Fluid dynamics is further 
divided into hydrodynamics, or the study of 
water flow, and aerodynamics, the study of air- 
flow. Applications of fluid mechanics include a 
variety of machines, ranging from the water- 
wheel to the airplane. In addition, the study of 
fluids provides an understanding of a number of 
everyday phenomena, such as why an open win- 
dow and door together create a draft in a room. 

H □ W IT WDRKS 

The Contrast Between Fluids 
and Solids 

To understand fluids, it is best to begin by con- 
trasting their behavior with that of solids. 
Whereas solids possess a definite volume and a 
definite shape, these physical characteristics are 
not so clearly defined for fluids. Liquids, though 
they possess a definite volume, have no definite 
shape — a factor noted above as one of the defin- 
ing characteristics of fluids. As for gases, they 
have neither a definite shape nor a definite vol- 
ume. 

One of several factors that distinguishes flu- 
ids from solids is their response to compression, 
or the application of pressure in such a way as to 

SCIENCE □ F EVERYDAY THINGS 


reduce the size or volume of an object. A solid is 
highly noncompressible, meaning that it resists 
compression, and if compressed with a sufficient 
force, its mechanical properties alter significant- 
ly. For example, if one places a drinking glass in a 
vise, it will resist a small amount of pressure, but 
a slight increase will cause the glass to break. 

Fluids vary with regard to compressibility, 
depending on whether the fluid in question is a 
liquid or a gas. Most gases tend to be highly com- 
pressible — though air, at low speeds at least, is 
not among them. Thus, gases such as propane 
fuel can be placed under high pressure. Liquids 
tend to be noncompressible: unlike a gas, a liquid 
can be compressed significantly, yet its response 
to compression is quite different from that of a 
solid — a fact illustrated below in the discussion 
of hydraulic presses. 

One way to describe a fluid is “anything that 
flows” — a behavior explained in large part by the 
interaction of molecules in fluids. If the surface 
of a solid is disturbed, it will resist, and if the 
force of the disturbance is sufficiently strong, it 
will deform — as for instance, when a steel plate 
begins to bend under pressure. This deformation 
will be permanent if the force is powerful 
enough, as was the case in the above example of 
the glass in a vise. By contrast, when the surface 
of a liquid is disturbed, it tends to flow. 

MDLECULAR BEHAVIDR OF 

fluids and SOLIDS. At the molecu- 
lar level, particles of solids tend to be definite in 
their arrangement and close to one another. In 
the case of liquids, molecules are close in prox- 
imity, though not as much so as solid molecules, 
and the arrangement is random. Thus, with a 
glass of water, the molecules of glass (which at 

VDLUME Z: REAL-LIFE PHYSICS 




In a wide, uncdnstricted region, a river flows slowly. However, if its flow is narrowed by canyon 
walls, as with Wyoming’s Bighorn River, then it speeds up dramatically. (Photograph by Kevin R. Morris/Corbis. 
Reproduced by permission.) 


96 


relatively low temperatures is a solid) in the con- 
tainer are fixed in place while the molecules of 
water contained by the glass are not. If one por- 
tion of the glass were moved to another place on 
the glass, this would change its structure. On the 
other hand, no significant alteration occurs in 
the character of the water if one portion of it is 
moved to another place within the entire volume 
of water in the glass. 

As for gas molecules, these are both random 
in arrangement and far removed in proximity. 
Whereas solid particles are slow-moving and 
have a strong attraction to one another, liquid 
molecules move at moderate speeds and exert a 
moderate attraction on each other. Gas mole- 
cules are extremely fast-moving and exert little or 
no attraction. 

Thus, if a solid is released from a container 
pointed downward, so that the force of gravity 
moves it, it will fall as one piece. Upon hitting a 
floor or other surface, it will either rebound, 
come to a stop, or deform permanently. A liquid, 
on the other hand, will disperse in response to 
impact, its force determining the area over which 
the total volume of liquid is distributed. But for a 
gas, assuming it is lighter than air, the downward 
pull of gravity is not even required to disperse it: 

VDLUME 2: REAL-LIFE PHYSICS 


once the top on a container of gas is released, the 
molecules begin to float outward. 

Fluids Under Pressure 

As suggested earlier, the response of fluids to 
pressure is one of the most significant aspects of 
fluid behavior and plays an important role with- 
in both the statics and dynamics subdisciplines 
of fluid mechanics. A number of interesting prin- 
ciples describe the response to pressure, on the 
part of both fluids at rest inside a container, and 
fluids which are in a state of flow. 

Within the realm of hydrostatics, among the 
most important of all statements describing the 
behavior of fluids is Pascal’s principle. This law is 
named after Blaise Pascal (1623-1662), a French 
mathematician and physicist who discovered that 
the external pressure applied on a fluid is trans- 
mitted uniformly throughout its entire body. The 
understanding offered by Pascal’s principle later 
became the basis for one of the most important 
machines ever developed, the hydraulic press. 

H YD R Q STATIC PRESSURE AND 

bud y a n c y. Some nineteen centuries before 
Pascal, the Greek mathematician, physicist, and 
inventor Archimedes (c. 287-212 b.c.) discovered 
a precept of fluid statics that had implications at 

SCIENCE DF EVERYDAY THINGS 


least as great as those of Pascal’s principle. This 
was Archimedes’s principle, which explains the 
buoyancy of an object immersed in fluid. 
According to Archimedes’s principle, the buoyant 
force exerted on the object is equal to the weight 
of the fluid it displaces. 

Buoyancy explains both how a ship floats on 
water, and how a balloon floats in the air. The 
pressures of water at the bottom of the ocean, 
and of air at the surface of Earth, are both exam- 
ples of hydrostatic pressure — the pressure that 
exists at any place in a body of fluid due to the 
weight of the fluid above. In the case of air pres- 
sure, air is pulled downward by the force of 
Earth’s gravitation, and air along the planet’s sur- 
face has greater pressure due to the weight of the 
air above it. At great heights above Earth’s sur- 
face, however, the gravitational force is dimin- 
ished, and thus the air pressure is much smaller. 

Water, too, is pulled downward by gravity, 
and as with air, the fluid at the bottom of the 
ocean has much greater pressure due to the 
weight of the fluid above it. Of course, water is 
much heavier than air, and therefore, water at 
even a moderate depth in the ocean has enor- 
mous pressure. This pressure, in turn, creates a 
buoyant force that pushes upward. 

If an object immersed in fluid — a balloon in 
the air, or a ship on the ocean — weighs less that 
the fluid it displaces, it will float. If it weighs 
more, it will sink or fall. The balloon itself maybe 
“heavier than air,” but it is not as heavy as the air 
it has displaced. Similarly, an aircraft carrier con- 
tains a vast weight in steel and other material, yet 
it floats, because its weight is not as great as that 
of the displaced water. 

BERNOULLI’S PRINCIPLE. Ar- 

chimedes and Pascal contributed greatly to what 
became known as fluid statics, but the father of 
fluid mechanics, as a larger realm of study, was 
the Swiss mathematician and physicist Daniel 
Bernoulli (1700-1782). While conducting exper- 
iments with liquids, Bernoulli observed that 
when the diameter of a pipe is reduced, the water 
flows faster. This suggested to him that some 
force must be acting upon the water, a force that 
he reasoned must arise from differences in pres- 
sure. 

Specifically, the slower-moving fluid in the 
wider area of pipe had a greater pressure than the 
portion of the fluid moving through the narrow- 
er part of the pipe. As a result, he concluded that 


pressure and velocity are inversely related — in 
other words, as one increases, the other decreas- 
es. Hence, he formulated Bernoulli’s principle, 
which states that for all changes in movement, 
the sum of static and dynamic pressure in a fluid 
remains the same. 

A fluid at rest exerts pressure — what 
Bernoulli called “static pressure” — on its con- 
tainer. As the fluid begins to move, however, a 
portion of the static pressure — proportional to 
the speed of the fluid — is converted to what 
Bernoulli called dynamic pressure, or the pres- 
sure of movement. In a cylindrical pipe, static 
pressure is exerted perpendicular to the surface 
of the container, whereas dynamic pressure is 
parallel to it. 

According to Bernoulli’s principle, the 
greater the velocity of flow in a fluid, the greater 
the dynamic pressure and the less the static pres- 
sure. In other words, slower-moving fluid exerts 
greater pressure than faster-moving fluid. The 
discovery of this principle ultimately made pos- 
sible the development of the airplane. 

REAL-LIFE 
A P P L I C AT I □ N S 

Bernoulli’s Principle in 
Action 

As fluid moves from a wider pipe to a narrower 
one, the volume of the fluid that moves a given 
distance in a given time period does not change. 
But since the width of the narrower pipe is small- 
er, the fluid must move faster (that is, with 
greater dynamic pressure) in order to move the 
same amount of fluid the same distance in the 
same amount of time. Observe the behavior of a 
river: in a wide, unconstricted region, it flows 
slowly, but if its flow is narrowed by canyon walls, 
it speeds up dramatically. 

Bernoulli’s principle ultimately became the 
basis for the airfoil, the design of an airplane’s 
wing when seen from the end. An airfoil is 
shaped like an asymmetrical teardrop laid on its 
side, with the “fat” end toward the airflow. As air 
hits the front of the airfoil, the airstream divides, 
part of it passing over the wing and part passing 
under. The upper surface of the airfoil is curved, 
however, whereas the lower surface is much 
straighten 


Fluid 
m ECHANICS 


97 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


Fluid 

Mechanics 


93 


As a result, the air flowing over the top has a 
greater distance to cover than the air flowing 
under the wing. Since fluids have a tendency to 
compensate for all objects with which they come 
into contact, the air at the top will flow faster to 
meet the other portion of the airstream, the air 
flowing past the bottom of the wing, when both 
reach the rear end of the airfoil. Faster airflow, as 
demonstrated by Bernoulli, indicates lower pres- 
sure, meaning that the pressure on the bottom of 
the wing keeps the airplane aloft. 

creating a draft. Among the 
most famous applications of Bernoulli’s princi- 
ple is its use in aerodynamics, and this is dis- 
cussed in the context of aerodynamics itself else- 
where in this book. Likewise, a number of other 
applications of Bernoulli’s principle are exam- 
ined in an essay devoted to that topic. Bernoulli’s 
principle, for instance, explains why a shower 
curtain tends to billow inward when the water is 
turned on; in addition, it shows why an open 
window and door together create a draft. 

Suppose one is in a hotel room where the 
heat is on too high, and there is no way to adjust 
the thermostat. Outside, however, the air is cold, 
and thus, by opening a window, one can presum- 
ably cool down the room. But if one opens the 
window without opening the front door of the 
room, there will be little temperature change. 
The only way to cool off will be by standing next 
to the window: elsewhere in the room, the air will 
be every bit as stuffy as before. But if the door 
leading to the hotel hallway is opened, a nice cool 
breeze will blow through the room. Why? 

With the door closed, the room constitutes 
an area of relatively high pressure compared to 
the pressure of the air outside the window. 
Because air is a fluid, it will tend to flow into the 
room, but once the pressure inside reaches a cer- 
tain point, it will prevent additional air from 
entering. The tendency of fluids is to move from 
high-pressure to low-pressure areas, not the 
other way around. As soon as the door is opened, 
the relatively high-pressure air of the room flows 
into the relatively low-pressure area of the hall- 
way. As a result, the air pressure in the room is 
reduced, and the air from outside can now enter. 
Soon a wind will begin to blow through the 
room. 

a wind tunnel. The above sce- 
nario of wind flowing through a room describes 
a rudimentary wind tunnel. A wind tunnel is a 

VDLUME 2: REAL-LIFE PHYSICS 


chamber built for the purpose of examining the 
characteristics of airflow in contact with solid 
objects, such as aircraft and automobiles. The 
wind tunnel represents a safe and judicious use 
of the properties of fluid mechanics. Its purpose 
is to test the interaction of airflow and solids in 
relative motion: in other words, either the air- 
craft has to be moving against the airflow, as it 
does in flight, or the airflow can be moving 
against a stationary aircraft. The first of these 
choices, of course, poses a number of dangers; on 
the other hand, there is little danger in exposing 
a stationary craft to winds at speeds simulating 
that of the aircraft in flight. 

The first wind tunnel was built in England in 
1871, and years later, aircraft pioneers Orville 
(1871-1948) and Wilbur (1867-1912) Wright 
used a wind tunnel to improve their planes. By 
the late 1930s, the U.S. National Advisory Com- 
mittee for Aeronautics (NACA) was building 
wind tunnels capable of creating speeds equal to 
300 MPH (480 km/h); but wind tunnels built 
after World War II made these look primitive. 
With the development of jet-powered flight, it 
became necessary to build wind tunnels capable 
of simulating winds at the speed of sound — 760 
MPH (340 m/s). By the 1950s, wind tunnels were 
being used to simulate hypersonic speeds — that 
is, speeds of Mach 5 (five times the speed of 
sound) and above. Researchers today use helium 
to create wind blasts at speeds up to Mach 50. 

Fluid Mechanics for Per- 
forming Work 

hydraulic presses. Though 
applications of Bernoulli’s principle are among 
the most dramatic examples of fluid mechanics 
in operation, the everyday world is filled with 
instances of other ideas at work. Pascal’s princi- 
ple, for instance, can be seen in the operation of 
any number of machines that represent varia- 
tions on the idea of a hydraulic press. Among 
these is the hydraulic jack used to raise a car off 
the floor of an auto mechanic’s shop. 

Beneath the floor of the shop is a chamber 
containing a quantity of fluid, and at either end 
of the chamber are two large cylinders side by 
side. Each cylinder holds a piston, and valves 
control flow between the two cylinders through 
the channel of fluid that connects them. In accor- 
dance with Pascal’s principle, when one applies 
force by pressing down the piston in one cylinder 

science df everyday things 


Fluid 

M ECHANICS 


(the input cylinder), this yields a uniform pres- 
sure that causes output in the second cylinder, 
pushing up a piston that raises the car. 

Another example of a hydraulic press is the 
hydraulic ram, which can be found in machines 
ranging from bulldozers to the hydraulic lifts 
used by firefighters and utility workers to reach 
heights. In a hydraulic ram, however, the charac- 
teristics of the input and output cylinders are 
reversed from those of a car jack. For the car jack, 
the input cylinder is long and narrow, while the 
output cylinder is wide and short. This is because 
the purpose of a car jack is to raise a heavy object 
through a relatively short vertical range of move- 
ment — just high enough so that the mechanic 
can stand comfortably underneath the car. 

In the hydraulic ram, the input or master 
cylinder is short and squat, while the output or 
slave cylinder is tall and narrow. This is because 
the hydraulic ram, in contrast to the car jack, car- 
ries a much lighter cargo (usually just one per- 
son) through a much greater vertical range — for 
instance, to the top of a tree or building. 

pumps. A pump is a device made for 
moving fluid, and it does so by utilizing a pres- 
sure difference, causing the fluid to move from 
an area of higher pressure to one of lower pres- 
sure. Its operation is based on aspects both of 
Pascal’s and Bernoulli’s principles — though, of 
course, humans were using pumps thousands of 
years before either man was born. 

A siphon hose used to draw gas from a car’s 
fuel tank is a very simple pump. Sucking on one 
end of the hose creates an area of low pressure 
compared to the relatively high-pressure area of 
the gas tank. Eventually, the gasoline will come 
out of the low-pressure end of the hose. 

The piston pump, slightly more complex, 
consists of a vertical cylinder along which a pis- 
ton rises and falls. Near the bottom of the cylin- 
der are two valves, an inlet valve through which 
fluid flows into the cylinder, and an outlet valve 
through which fluid flows out. As the piston 
moves upward, the inlet valve opens and allows 
fluid to enter the cylinder. On the downstroke, 
the inlet valve closes while the outlet valve opens, 
and the pressure provided by the piston forces 
the fluid through the outlet valve. 

One of the most obvious applications of the 
piston pump is in the engine of an automobile. 
In this case, of course, the fluid being pumped is 
gasoline, which pushes the pistons up and down 

SCIENCE □ F EVERYDAY THINGS 


r ' -*> 



Pumps for drawing usable water from the 

GROUND ARE UNDOUBTEDLY THE OLDEST PUMPS 

known. (Photograph by Richard Cummins/Corbis. Reproduced by 
permission.) 

by providing a series of controlled explosions 
created by the spark plug’s ignition of the gas. In 
another variety of piston pump — the kind used 
to inflate a basketball or a bicycle tire — air is the 
fluid being pumped. Then there is a pump for 
water. Pumps for drawing usable water from the 
ground are undoubtedly the oldest known vari- 
ety, but there are also pumps designed to remove 
water from areas where it is undesirable; for 
example, a bilge pump, for removing water from 
a boat, or the sump pump used to pump flood 
water out of a basement. 

fluid power. For several thousand 
years, humans have used fluids — in particular 
water — to power a number of devices. One of the 
great engineering achievements of ancient times 
was the development of the waterwheel, which 
included a series of buckets along the rim that 
made it possible to raise water from the river 
below and disperse it to other points. By about 70 
b.c., Roman engineers recognized that they could 
use the power of water itself to turn wheels and 
grind grain. Thus, the waterwheel became one of 
the first mechanisms in which an inanimate 

VDLUME 2: REAL-LIFE PHYSICS 


99 


Fluid 

Mechanics 


KEY TERMS 


aerodynamics: An area of fluid 

dynamics devoted to studying the proper- 
ties and characteristics of airflow. 

ARCHIMEDES’S PRINCIPLE: A rule 

of physics stating that the buoyant force of 
an object immersed in fluid is equal to the 
weight of the fluid displaced by the object. 
It is named after the Greek mathematician, 
physicist, and inventor, Archimedes (c. 
287-212 b.c.), who first identified it. 

Bernoulli’s principle: A prop- 

osition, credited to Swiss mathematician 
and physicist Daniel Bernoulli (1700- 
1782), which maintains that slower-mov- 
ing fluid exerts greater pressure than faster- 
moving fluid. 

buoyancy: The tendency of an object 

immersed in a fluid to float. This can be 
explained by Archimedes’s principle. 

compression: To reduce in size or 

volume by applying pressure. 

fluid: Any substance, whether gas or 

liquid, that conforms to the shape of its 
container. 

fluid dynamics: An area of fluid 

mechanics devoted to studying of the 
behavior of moving, or flowing, fluids. 
Fluid dynamics is further divided into 
hydrodynamics and aerodynamics. 

fluid mechanics: The study of 

the behavior of gases and liquids at rest 
and in motion. The major divisions of 


fluid mechanics are fluid statics and fluid 
dynamics. 

fluid statics: An area of fluid 

mechanics devoted to studying the behav- 
ior of stationary fluids. 

hydrodynamics: An area of fluid 

dynamics devoted to studying the proper- 
ties and characteristics of water flow. 

HYDRDSTATIC PRESSURE: The 

pressure that exists at any place in a body of 
fluid due to the weight of the fluid above. 

pascal’s principle: A statement, 

formulated by French mathematician and 
physicist Blaise Pascal (1623-1662), which 
holds that the external pressure applied on 
a fluid is transmitted uniformly through- 
out the entire body of that fluid. 

pressure: The ratio of force to sur- 

face area, when force is applied in a direc- 
tion perpendicular to that surface. 

turbine: A machine that converts the 

kinetic energy (the energy of movement) 
in fluids to useable mechanical energy by 
passing the stream of fluid through a series 
of fixed and moving fans or blades. 

wind tunnel: A chamber built for 

the purpose of examining the characteris- 
tics of airflow in relative motion against 
solid objects such as aircraft and auto- 
mobiles. 


| l □□ 


source (as opposed to the effort of humans or 
animals) created power. 

The water clock, too, was another ingenious 
use of water developed by the ancients. It did not 
use water for power; rather, it relied on gravity — 
a concept only dimly understood by ancient peo- 

vdlume z: real-life physics 


pies — to move water from one chamber of the 
clock to another, thus, marking a specific interval 
of time. The earliest clocks were sundials, which 
were effective for measuring time, provided the 
Sun was shining, but which were less useful for 
measuring periods shorter than an hour. Hence, 

SCIENCE DF EVERYDAY THINGS 



the development of the hourglass, which used 
sand, a solid that in larger quantities exhibits the 
behavior of a fluid. Then, in about 270 b.c., Cte- 
sibius of Alexandria (fl. c. 270-250 b.c.) used 
gearwheel technology to devise a constant- flow 
water clock called a “clepsydra.” Use of water 
clocks prevailed for more than a thousand years, 
until the advent of the first mechanical clocks. 

During the medieval period, fluids provided 
power to windmills and water mills, and at the 
dawn of the Industrial Age, engineers began 
applying fluid principles to a number of sophis- 
ticated machines. Among these was the turbine, a 
machine that converts the kinetic energy (the 
energy of movement) in fluids to useable 
mechanical energy by passing the stream of fluid 
through a series of fixed and moving fans or 
blades. A common house fan is an example of a 
turbine in reverse: the fan adds energy to the 
passing fluid (air), whereas a turbine extracts 
energy from fluids such as air and water. 

The turbine was developed in the mid-eigh- 
teenth century, and later it was applied to the 
extraction of power from hydroelectric dams, the 
first of which was constructed in 1894. Today, 
hydroelectric dams provide electric power to 
millions of homes around the world. Among the 
most dramatic examples of fluid mechanics in 
action, hydroelectric dams are vast in size and 
equally impressive in the power they can generate 
using a completely renewable resource: water. 

A hydroelectric dam forms a huge steel-and- 
concrete curtain that holds back millions of tons 
of water from a river or other body. The water 


nearest the top — the “head” of the dam — has 
enormous potential energy, or the energy that an 
object possesses by virtue of its position. Hydro- 
electric power is created by allowing controlled 
streams of this water to flow downward, gather- 
ing kinetic energy that is then transferred to 
powering turbines, which in turn generate elec- 
tric power. 

WHERE TD LEARN MORE 

Aerodynamics for Students (Web site). 

<http://www.ae.su.oz.au/aero/contents.html> (April 

8 , 2001 ). 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Science 
for Curious Minds. Illustrated by Ann Humphrey 
Williams. Hauppauge, N.Y.: Barron’s, 2000. 

“Educational Fluid Mechanics Sites.” Virginia Institute of 
Technology (Web site), <http://www.eng.vt.edu/flu- 
ids/links/edulinks.htm> (April 8, 2001). 

Fleisher, Paul. Liquids and Gases: Principles of Fluid 
Mechanics. Minneapolis, MN: Lerner Publications, 
2002. 

Institute of Fluid Mechanics (Web site). 

<http://www.ts.go.dlr.de> (April 8, 2001). 

K8AIT Principles of Aeronautics Advanced Text (web site). 
<http://wings.ucdavis.edu/Book/advanced.html> 
(February 19, 2001). 

Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

Sobey, Edwin J. C. Wacky Water Fun with Science: Science 
You Can Float, Sink, Squirt, and Sail. Illustrated by 
Bill Burg. New York: McGraw-Hill, 2000. 

Wood, Robert W. Mechanics Fundamentals. Illustrated by 
Bill Wright. Philadelphia: Chelsea House, 1997. 


Fluid 

M ECHANICS 


SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 □ 1 


AERODYNAMICS 


| i az 


C □ N C E PT 

Though the term “aerodynamics” is most com- 
monly associated with airplanes and the overall 
science of flight, in fact, its application is much 
broader. Simply put, aerodynamics is the study of 
airflow and its principles, and applied aerody- 
namics is the science of improving manmade 
objects such as airplanes and automobiles in light 
of those principles. Aside from the obvious appli- 
cation to these heavy forms of transportation, 
aerodynamic concepts are also reflected in the 
simplest of manmade flying objects — and in the 
natural model for all studies of flight, a bird’s 
wings. 

H □ W IT WORKS 

All physical objects on Earth are subject to grav- 
ity, but gravity is not the only force that tends to 
keep them pressed to the ground. The air itself, 
though it is invisible, operates in such a way as to 
prevent lift, much as a stone dropped into the 
water will eventually fall to the bottom. In fact, 
air behaves much like water, though the down- 
ward force is not as great due to the fact that air’s 
pressure is much less than that of water. Yet both 
are media through which bodies travel, and air 
and water have much more in common with one 
another than either does with a vacuum. 

Liquids such as water and gasses such as air 
are both subject to the principles of fluid dynam- 
ics, a set of laws that govern the motion of liquids 
and vapors when they come in contact with solid 
surfaces. In fact, there are few significant differ- 
ences — for the purposes of the present discus- 
sion — between water and air with regard to their 
behavior in contact with solid surfaces. 

VDLUME 2: REAL-LIFE PHYSICS 


When a person gets into a bathtub, the water 
level rises uniformly in response to the fact that a 
solid object is taking up space. Similarly, air cur- 
rents blow over the wings of a flying aircraft in 
such a way that they meet again more or less 
simultaneously at the trailing edge of the wing. 
In both cases, the medium adjusts for the intru- 
sion of a solid object. Hence within the parame- 
ters of fluid dynamics, scientists typically use the 
term “fluid” uniformly, even when describing the 
movement of air. 

The study of fluid dynamics in general, and 
of air flow in particular, brings with it an entire 
vocabulary. One of the first concepts of impor- 
tance is viscosity, the internal friction in a fluid 
that makes it resistant to flow and resistant to 
objects flowing through it. As one might suspect, 
viscosity is a far greater factor with water than 
with air, the viscosity of which is less than two 
percent that of water. Nonetheless, near a solid 
surface — for example, the wing of an airplane — 
viscosity becomes a factor because air tends to 
stick to that surface. 

Also significant are the related aspects of 
density and compressibility. At speeds below 220 
MPH (354 km/h), the compressibility of air is 
not a significant factor in aerodynamic design. 
However, as air flow approaches the speed of 
sound — 660 MPH (1,622 km/h) — compressibil- 
ity becomes a significant factor. Likewise temper- 
ature increases greatly when airflow is superson- 
ic, or faster than the speed of sound. 

All objects in the air are subject to two types 
of airflow, laminar and turbulent. Laminar flow 
is smooth and regular, always moving at the same 
speed and in the same direction. This type of air- 
flow is also known as streamlined flow, and 
under these conditions every particle of fluid that 

SCIENCE □ F EVERYDAY THINGS 



passes a particular point follows a path identical 
to all particles that passed that point earlier. This 
may be illustrated by imagining a stream flowing 
around a twig. 

By contrast, in turbulent flow the air is sub- 
ject to continual changes in speed and direc- 
tion — as for instance when a stream flows over 
shoals of rocks. Whereas the mathematical model 
of laminar airflow is rather straightforward, con- 
ditions are much more complex in turbulent 
flow, which typically occurs in the presence 
either of obstacles or of high speeds. 

Absent the presence of viscosity, and thus in 
conditions of perfect laminar flow, an object 
behaves according to Bernoulli’s principle, some- 
times known as Bernoulli’s equation. Named after 
the Swiss mathematician and physicist Daniel 
Bernoulli (1700-1782), this proposition goes to 
the heart of that which makes an airplane fly. 

While conducting experiments concerning 
the conservation of energy in liquids, Bernoulli 
observed that when the diameter of a pipe is 
reduced, the water flows faster. This suggested to 
him that some force must be acting upon the 
water, a force that he reasoned must arise from 
differences in pressure. Specifically, the slower- 
moving fluid had a greater pressure than the por- 
tion of the fluid moving through the narrower 
part of the pipe. As a result, he concluded that 
pressure and velocity are inversely related. 

Bernoulli’s principle states that for all 
changes in movement, the sum of static and 
dynamic pressure in a fluid remain the same. A 
fluid at rest exerts static pressure, which is the 
same as what people commonly mean when they 
say “pressure,” as in “water pressure.” As the fluid 
begins to move, however, a portion of the static 
pressure — proportional to the speed of the 
fluid — is converted to what scientists call dynam- 
ic pressure, or the pressure of movement. The 
greater the speed, the greater the dynamic pres- 
sure and the less the static pressure. Bernoulli’s 
findings would prove crucial to the design of air- 
craft in the twentieth century, as engineers 
learned how to use currents of faster and slower 
air for keeping an airplane aloft. 

Very close to the surface of an object experi- 
encing airflow, however, the presence of viscosity 
plays havoc with the neat proportions of the 
Bernoulli’s principle. Here the air sticks to the 
object’s surface, slowing the flow of nearby air 
and creating a “boundary layer” of slow-moving 

SCIENCE □ E EVERYDAY THINGS 



A TYPICAL PAPER AIRPLANE HAS LOW ASPECT RATI □ 
WINGS, A TERM THAT REFERS TG THE SIZE OF THE 
WINGSPAN COMPARED TO THE CHORD. IN SUBSONIC 
FLIGHT, HIGHER ASPECT RATIOS ARE USUALLY PRE- 
FERRED. (Photograph by Bruce Burkhardt/Corbis. Reproduced by per- 
mission.) 

air. At the beginning of the flow — for instance, at 
the leading edge of an airplane’s wing — this 
boundary layer describes a laminar flow; but the 
width of the layer increases as the air moves 
along the surface, and at some point it becomes 
turbulent. 

These and a number of other factors con- 
tribute to the coefficients of drag and lift. Simply 
put, drag is the force that opposes the forward 
motion of an object in airflow, whereas lift is a 
force perpendicular to the direction of the wind, 
which keeps the object aloft. Clearly these con- 
cepts can be readily applied to the operation of 
an airplane, but they also apply in the case of an 
automobile, as will be shown later. 

REAL-LIFE 
A P P L I C AT I □ N S 

How a Bird Flies — and Why a 
Human Being Cannot 

Birds are exquisitely designed (or adapted) for 
flight, and not simply because of the obvious fact 

VDLUME 2: REAL-LIFE PHYSICS 


Aero- 

dynamics 


1 □ 3 


Aero- 

dynamics 


| 1 D4 



Birds like these fairy terns are supreme examples of aerodynamic principles, from their low body 
weight and large sternum and pectoralis muscles to their lightweight feathers. (Corbis. Reproduced by per- 
mission.) 


that they have wings. Thanks to light, hollow 
bones, their body weight is relatively low, giving 
them the advantage in overcoming gravity and 
remaining aloft. Furthermore, a bird’s sternum 
or breast bone, as well as its pectoralis muscles 
(those around the chest) are enormous in pro- 
portion to its body size, thus helping it to achieve 
the thrust necessary for flight. And finally, the 
bird’s lightweight feathers help to provide opti- 
mal lift and minimal drag. 

A bird’s wing is curved along the top, a cru- 
cial aspect of its construction. As air passes over 
the leading edge of the wing, it divides, and 
because of the curve, the air on top must travel a 
greater distance before meeting the air that 
flowed across the bottom. The tendency of air- 
flow, as noted earlier, is to correct for the presence 
of solid objects. Therefore, in the absence of out- 
side factors such as viscosity, the air on top “tries” 
to travel over the wing in the same amount of 
time that it takes the air below to travel under the 
wing. As shown by Bernoulli, the fast-moving air 
above the wing exerts less pressure than the slow- 
moving air below it; hence there is a difference in 
pressure between the air below and the air above, 
and this keeps the wing aloft. 

VDLUME 2: REAL-LIFE PHYSICS 


When a bird beats its wings, its downstrokes 
propel it, and as it rises above the ground, the 
force of aerodynamic lift helps push its wings 
upward in preparation for the next downstroke. 
However, to reduce aerodynamic drag during the 
upstroke, the bird folds its wings, thus decreasing 
its wingspan. Another trick that birds execute 
instinctively is the moving of their wings forward 
and backward in order to provide balance. They 
also “know” how to flap their wings in a direction 
almost parallel to the ground when they need to 
fly slowly or hover. 

Witnessing the astonishing aerodynamic 
feats of birds, humans sought the elusive goal of 
flight from the earliest of times. This was sym- 
bolized by the Greek myth of Icarus and 
Daedalus, who escaped from a prison in Crete by 
constructing a set of bird-like wings and flying 
away. In the world of physical reality, however, 
the goal would turn out to be unattainable as 
long as humans attempted to achieve flight by 
imitating birds. 

As noted earlier, a bird’s physiology is quite 
different from that of a human being. There is 
simply no way that a human can fly by flapping 
his arms — nor will there ever be a man strong 
enough to do so, no matter how apparently well- 

SCIENCE □ F EVERYDAY THINGS 



designed his mechanical wings are. Indeed, to be 
capable of flying like a bird, a man would have to 
have a chest so enormous in proportion to his 
body that he would be hideous in appearance. 

Not realizing this, humans for centuries 
attempted to fly like birds — with disastrous 
results. An English monk named Eilmer (b. 980) 
attempted to fly off the tower of Malmesbury 
Abbey with a set of wings attached to his arms 
and feet. Apparently Eilmer panicked after glid- 
ing some 600 ft (about 200 m) and suddenly 
plummeted to earth, breaking both of his legs. At 
least he lived; more tragic was the case of Abul 
Qasim Ibn Firnas (d. 873), an inventor from Cor- 
doba in Arab Spain who devised and demon- 
strated a glider. Much of Cordoba’s population 
came out to see him demonstrate his flying 
machine, but after covering just a short distance, 
the craft fell to earth. Severely wounded, Ibn Fir- 
nas died shortly afterward. 

The first real progress in the development of 
flying machines came when designers stopped 
trying to imitate birds and instead used the prin- 
ciple of buoyancy. Hence in 1783, the French 
brothers Jacques-Etienne and Joseph-Michel 
Montgolfier constructed the first practical bal- 
loon. 

Balloons and their twentieth-century 
descendant, the dirigible, had a number of obvi- 
ous drawbacks, however. Without a motor, a bal- 
loon could not be guided, and even with a motor, 
dirigibles proved highly dangerous. At that stage, 
most dirigibles used hydrogen, a gas that is cheap 
and plentiful, but extremely flammable. After the 
Hindenburg exploded in 1937, the age of passen- 
ger travel aboard airships was over. 

However, the German military continued to 
use dirigibles for observation purposes, as did the 
United States forces in World War II. Today air- 
ships, the most famous example being the 
Goodyear Blimp, are used not only for observa- 
tion but for advertising. Scientists working in 
rain forests, for instance, use dirigibles to glide 
above the forest canopy; as for the Goodyear 
Blimp, it provides television networks with “eye 
in the sky” views of large sporting events. 

The first man to make a serious attempt at 
creating a heavier-than-air flying machine (as 
opposed to a balloon, which uses gases that are 
lighter than air) was Sir George Cayley (1773- 
1857), who in 1853 constructed a glider. It is 
interesting to note that in creating this, the fore- 

SCIENCE □ E EVERYDAY THINGS 


runner of the modern airplane, Cayley went back 
to an old model: the bird. After studying the 
physics of birds’ flight for many years, he 
equipped his glider with an extremely wide 
wingspan, used the lightest possible materials in 
its construction, and designed it with exception- 
ally smooth surfaces to reduce drag. 

The only thing that in principle differentiat- 
ed Cayley’s craft from a modern airplane was its 
lack of an engine. In those days, the only possible 
source of power was a steam engine, which 
would have added far too much weight to his air- 
craft. However, the development of the internal- 
combustion engine in the nineteenth century 
overcame that obstacle, and in 1903 Orville and 
Wilbur Wright achieved the dream of flight that 
had intrigued and eluded human beings for cen- 
turies. 

Airplanes: Getting Aloft, 
Staying Aloft, and Remaining 
Stable 

Once engineers and pilots took to the air, they 
encountered a number of factors that affect 
flight. In getting aloft and staying aloft, an air- 
craft is subject to weight, lift, drag, and thrust. 

As noted earlier, the design of an airplane 
wing takes advantage of Bernoulli’s principle to 
give it lift. Seen from the end, the wing has the 
shape of a long teardrop lying on its side, with 
the large end forward, in the direction of airflow, 
and the narrow tip pointing toward the rear. 
(Unlike a teardrop, however, an airplane’s wing is 
asymmetrical, and the bottom side is flat.) This 
cross-section is known as an airfoil, and the 
greater curvature of its upper surface in compar- 
ison to the lower side is referred to as the air- 
plane’s camber. The front end of the airfoil is also 
curved, and the chord line is an imaginary 
straight line connecting the spot where the air 
hits the front — known as the stagnation point — 
to the rear, or trailing edge, of the wing. 

Again in accordance with Bernoulli’s princi- 
ple, the shape of the airflow facilitates the spread 
of laminar flow around it. The slower-moving 
currents beneath the airfoil exert greater pressure 
than the faster currents above it, giving lift to the 
aircraft. 

Another parameter influencing the lift coef- 
ficient (that is, the degree to which the aircraft 
experiences lift) is the size of the wing: the longer 
the wing, the greater the total force exerted 

VDLUME Z : REAL-LIFE PHYSICS 


Aero- 

dynamics 


1 □ 5 


Aero- 

dynamics 


I 1 □ s 


beneath it, and the greater the ratio of this pres- 
sure to that of the air above. The size of a mod- 
ern aircraft’s wing is actually somewhat variable, 
due to the presence of flaps at the trailing edge. 

With regard to the flaps, however, it should 
be noted that they have different properties at 
different stages of flight: in takeoff, they provide 
lift, but in stable flight they increase drag, and for 
that reason the pilot retracts them. In preparing 
for landing, as the aircraft slows and descends, 
the extended flaps then provide stability and 
assist in the decrease of speed. 

Speed, too, encourages lift: the faster the 
craft, the faster the air moves over the wing. The 
pilot affects this by increasing or decreasing the 
power of the engine, thus regulating the speed 
with which the plane’s propellers turn. Another 
highly significant component of lift is the airfoil’s 
angle of attack — the orientation of the airfoil 
with regard to the air flow, or the angle that the 
chord line forms with the direction of the air 
stream. 

Up to a point, increasing the angle of attack 
provides the aircraft with extra lift because it 
moves the stagnation point from the leading 
edge down along the lower surface; this increases 
the low-pressure area of the upper surface. How- 
ever, if the pilot increases the angle of attack too 
much, this affects the boundary layer of slow- 
moving air, causing the aircraft to go into a stall. 

Together the engine provides the propellers 
with power, and this gives the aircraft thrust, or 
propulsive force. In fact, the propeller blades 
constitute miniature wings, pivoted at the center 
and powered by the engine to provide rotational 
motion. As with the wings of the aircraft, the 
blades have a convex forward surface and a nar- 
row trailing edge. Also like the aircraft wings, 
their angle of attack (or pitch) is adjusted at dif- 
ferent points for differing effects. In stable flight, 
the pilot increases the angle of attack for the pro- 
peller blades sharply as against airflow, whereas 
at takeoff and landing the pitch is dramatically 
reduced. During landing, in fact, the pilot actual- 
ly reverses the direction of the propeller blades, 
turning them into a brake on the aircraft’s for- 
ward motion — and producing that lurching sen- 
sation that a passenger experiences as the aircraft 
slows after touching down. 

By this point there have been several exam- 
ples regarding the use of the same technique 
alternately to provide lift or — when slowing or 

VDLUME 2: REAL-LIFE PHYSICS 


preparing to land — drag. This apparent inconsis- 
tency results from the fact that the characteristics 
of air flow change drastically from situation to 
situation, and in fact, air never behaves as per- 
fectly as it does in a textbook illustration of 
Bernoulli’s principle. 

Not only is the aircraft subject to air viscosi- 
ty — the air’s own friction with itself — it also 
experiences friction drag, which results from the 
fact that no solid can move through a fluid with- 
out experiencing a retarding force. An even 
greater drag factor, accounting for one-third of 
that which an aircraft experiences, is induced 
drag. The latter results because air does not flow 
in perfect laminar streams over the airfoil; rather, 
it forms turbulent eddies and currents that act 
against the forward movement of the plane. 

In the air, an aircraft experiences forces that 
tend to destabilize flight in each of three dimen- 
sions. Pitch is the tendency to rotate forward or 
backward; yaw, the tendency to rotate on a hori- 
zontal plane; and roll, the tendency to rotate ver- 
tically on the axis of its fuselage. Obviously, each 
of these is a terrifying prospect, but fortunately, 
pilots have a solution for each. To prevent pitch- 
ing, they adjust the angle of attack of the hori- 
zontal tail at the rear of the craft. The vertical rear 
tail plays a part in preventing yawing, and to pre- 
vent rolling, the pilot raises the tips of the main 
wings so that the craft assumes a V-shape when 
seen from the front or back. 

The above factors of lift, drag, thrust, and 
weight, as well as the three types of possible 
destabilization, affect all forms of heavier-than- 
air flying machines. But since the 1944 advent of 
jet engines, which travel much faster than piston- 
driven engines, planes have flown faster and 
faster, and today some craft such as the Concorde 
are capable of supersonic flight. In these situa- 
tions, air compressibility becomes a significant 
issue. 

Sound is transmitted by the successive com- 
pression and expansion of air. But when a plane 
is traveling at above Mach 1.2 — the Mach num- 
ber indicates the speed of an aircraft in relation 
to the speed of sound — there is a significant dis- 
crepancy between the speed at which sound is 
traveling away from the craft, and the speed at 
which the craft is moving away from the sound. 
Eventually the compressed sound waves build up, 
resulting in a shock wave. 

SCIENCE OF EVERYDAY THINGS 


Down on the ground, the shock wave mani- 
fests as a “sonic boom”; meanwhile, for the air- 
craft, it can cause sudden changes in pressure, 
density, and temperature, as well as an increase in 
drag and a loss of stability. To counteract this 
effect, designers of supersonic and hypersonic 
(Mach 5 and above) aircraft are altering wing 
design, using a much narrower airfoil and swept- 
back wings. 

One of the pioneers in this area is Richard 
Whitcomb of the National Aeronautics and 
Space Administration (NASA). Whitcomb has 
designed a supercritical airfoil for a proposed 
hypersonic plane, which would ascend into outer 
space in the course of a two-hour flight — all the 
time needed for it to travel from Washington, 
D.C., to Tokyo, Japan. Before the craft can 
become operational, however, researchers will 
have to figure out ways to control temperatures 
and keep the plane from bursting into flame as it 
reenters the atmosphere. 

Much of the research for improving the 
aerodynamic qualities of such aircraft takes place 
in wind tunnels. First developed in 1871, these 
use powerful fans to create strong air currents, 
and over the years the top speed in wind tunnels 
has been increased to accommodate testing on 
supersonic and hypersonic aircraft. Researchers 
today use helium to create wind blasts at speeds 
up to Mach 50. 

Thrdwn and Flown: The Aero- 
dynamics of Small Objects 

Long before engineers began to dream of sending 
planes into space for transoceanic flight — about 
14,000 years ago, in fact — many of the features 
that make an airplane fly were already present in 
the boomerang. It might seem backward to move 
from a hypersonic jet to a boomerang, but in 
fact, it is easier to appreciate the aerodynamics of 
small objects, including the kite and even the 
paper airplane, once one comprehends the larger 
picture. 

There is a certain delicious irony in the fact 
that the first manmade object to take flight was 
constructed by people who never advanced 
beyond the Stone Age until the nineteenth centu- 
ry, when the Europeans arrived in Australia. As 
the ethnobotanist Jared Diamond showed in his 
groundbreaking work Guns, Germs, and Steel: 
The Fates of Human Societies (1997), this was not 
because the Aborigines of Australia were less 

SCIENCE □ F EVERYDAY THINGS 


intelligent than Europeans. In fact, as Diamond 
showed, an individual would actually have to be 
smarter to figure out how to survive on the lim- 
ited range of plants and animals available in Aus- 
tralia prior to the introduction of Eurasian flora 
and fauna. Hence the wonder of the boomerang, 
one of the most ingenious inventions ever fash- 
ioned by humans in a “primitive” state. 

Thousands of years before Bernoulli, the 
boomerang’s designers created an airfoil consis- 
tent with Bernoulli’s principle. The air below 
exerts more pressure than the air above, and this, 
combined with the factors of gyroscopic stability 
and gyroscopic precession, gives the boomerang 
flight. 

Gyroscopic stability can be illustrated by 
spinning a top: the action of spinning itself keeps 
the top stable. Gyroscopic precession is a much 
more complex process: simply put, the leading 
wing of the boomerang — the forward or upward 
edge as it spins through the air — creates more lift 
than the other wing. At this point it should be 
noted that, contrary to the popular image, a 
boomerang travels on a plane perpendicular to 
that of the ground, not parallel. Hence any 
thrower who knows what he or she is doing toss- 
es the boomerang not with a side-arm throw, but 
overhand. 

And of course a boomerang does not just 
sail through the air; a skilled thrower can make it 
come back as if by magic. This is because the 
force of the increased lift that it experiences in 
flight, combined with gyroscopic precession, 
turns it around. As noted earlier, in different sit- 
uations the same force that creates lift can create 
drag, and as the boomerang spins downward the 
increasing drag slows it. Certainly it takes great 
skill for a thrower to make a boomerang come 
back, and for this reason, participants in 
boomerang competitions often attach devices 
such as flaps to increase drag on the return cycle. 

Another very early example of an aerody- 
namically sophisticated humanmade device — 
though it is quite recent compared to the 
boomerang — is the kite, which first appeared in 
China in about 1000 b.c. The kite’s design bor- 
rows from avian anatomy, particularly the bird’s 
light, hollow bones. Hence a kite, in its simplest 
form, consists of two crossed strips of very light 
wood such as balsa, with a lightweight fabric 
stretched over them. 

VDLUME 2: REAL-LIFE PHYSICS 


Aero- 

dynamics 


1 □ 7 


Aero- 

dynamics 


I 1 PS 


Kites can come in a variety of shapes, though 
for many years the well-known diamond shape 
has been the most popular, in part because its 
aerodynamic qualities make it easiest for the 
novice kite-flyer to handle. Like birds and 
boomerangs, kites can “fly” because of the physi- 
cal laws embodied in Bernoulli’s principle: at the 
best possible angle of attack, the kite experiences 
a maximal ratio of pressure from the slower- 
moving air below as against the faster-moving air 
above. 

For centuries, when the kite represented the 
only way to put a humanmade object many hun- 
dreds of feet into the air, scientists and engineers 
used them for a variety of experiments. Of 
course, the most famous example of this was 
Benjamin Franklin’s 1752 experiment with elec- 
tricity. More significant to the future of aerody- 
namics were investigations made half a century 
later by Cayley, who recognized that the kite, 
rather than the balloon, was an appropriate 
model for the type of heavier-than-air flight he 
intended. 

In later years, engineers built larger kites 
capable of lifting men into the air, but the advent 
of the airplane rendered kites obsolete for this 
purpose. However, in the 1950s an American 
engineer named Francis Rogallo invented the 
flexible kite, which in turn spawned the delta 
wing kite used by hang gliders. During the 1960s, 
Domina Jolbert created the parafoil, an even 
more efficient device, which took nonmecha- 
nized human flight perhaps as far as it can go. 

Akin to the kite, glider, and hang glider is 
that creation of childhood fancy, the paper air- 
plane. In its most basic form — and paper air- 
plane enthusiasts are capable of fairly complex 
designs — a paper airplane is little more than a set 
of wings. There are a number or reasons for this, 
not least the fact that in most cases, a person fly- 
ing a paper airplane is not as concerned about 
pitch, yaw, and roll as a pilot flying with several 
hundred passengers on board would be. 

However, when fashioning a paper airplane 
it is possible to add a number of design features, 
for instance by folding flaps upward at the tail. 
These become the equivalent of the elevator, a 
control surface along the horizontal edge of a real 
aircraft’s tail, which the pilot rotates upward to 
provide stability. But as noted by Ken Blackburn, 
author of several books on paper airplanes, it is 
not necessarily the case that an airplane must 

VDLUME 2: REAL-LIFE PHYSICS 


have a tail; indeed, some of the most sophisticat- 
ed craft in the sky today — including the fearsome 
B-2 “Stealth” bomber — do not have tails. 

A typical paper airplane has low aspect ratio 
wings, a term that refers to the size of the 
wingspan compared to the chord line. In subson- 
ic flight, higher aspect ratios are usually pre- 
ferred, and this is certainly the case with most 
“real” gliders; hence their wings are longer, and 
their chord lines shorter. But there are several 
reasons why this is not the case with a paper air- 
plane. 

First of all, as Blackburn noted wryly on his 
Web site, “Paper is a lousy building material. 
There is a reason why real airplanes are not made 
of paper.” He stated the other factors governing 
paper airplanes’ low aspect ratio in similarly 
whimsical terms. First, “Low aspect ratio wings 
are easier to fold....”; second, “Paper airplane 
gliding performance is not usually very impor- 
tant....”; and third, “Low-aspect ratio wings look 
faster, especially if they are swept back.” 

The reason why low-aspect ratio wings look 
faster, Blackburn suggested, is that people see 
them on jet fighters and the Concorde, and 
assume that a relatively narrow wing span with a 
long chord line yields the fastest speeds. And 
indeed they do — but only at supersonic speeds. 
Below the speed of sound, high-aspect ratio 
wings are best for preventing drag. Furthermore, 
as Blackburn went on to note, low-aspect ratio 
wings help the paper airplane to withstand the 
relatively high launch speeds necessary to send 
them into longer glides. 

In fact, a paper airplane is not subject to any- 
thing like the sort of design constraints affecting 
a real craft. All real planes look somewhat similar, 
because the established combinations, ratios, and 
dimensions of wings, tails, and fuselage work 
best. Certainly there is a difference in basic 
appearance between subsonic and supersonic 
aircraft — but again, all supersonic jets have more 
or less the same low-aspect, swept wing. “With 
paper airplanes,” Blackburn wrote, “it’s easy to 
make airplanes that don’t look like real airplanes” 
since “The mission of a paper airplane is [simply] 
to provide a good time for the pilot.” 

Aerodynamics on the Ground 

The preceding discussions of aerodynamics in 
action have concerned the behavior of objects off 
the ground. But aerodynamics is also a factor in 

SCIENCE OF EVERYDAY THINGS 


wheeled transport on Earth’s surface, whether by 
bicycle, automobile, or some other variation. 

On a bicycle, the rider accounts for 65-80% 
of the drag, and therefore his or her position with 
regard to airflow is highly important. Thus, from 
as early as the 1890s, designers of racing bikes 
have favored drop handlebars, as well as a seat 
and frame that allow a crouched position. Since 
the 1980s, bicycle designers have worked to elim- 
inate all possible extra lines and barriers to air- 
flow, including the crossbar and chainstays. 

A typical bicycle’s wheel contains 32 or 36 
cylindrical spokes, and these can affect aerody- 
namics adversely. As the wheel rotates, the air- 
flow behind the spoke separates, creating turbu- 
lence and hence drag. For this reason, some of 
the most advanced bicycles today use either aero- 
dynamic rims, which reduce the length of the 
spokes, three-spoke aerodynamic wheels, or even 
solid wheels. 

The rider’s gear can also serve to impede or 
enhance his velocity, and thus modern racing 
helmets have a streamlined shape — rather like 
that of an airfoil. The best riders, such as those 
who compete in the Olympics or the Tour de 
France, have bikes custom-designed to fit their 
own body shape. 

One interesting aspect of aerodynamics 
where it concerns bicycle racing is the phenome- 
non of “drafting.” Riders at the front of a pack, 
like riders pedaling alone, consume 30-40% 
more energy than do riders in the middle of a 
pack. The latter are benefiting from the efforts of 
bicyclists in front of them, who put up most 
of the wind resistance. The same is true for 
bicyclists who ride behind automobiles or 
motorcycles. 

The use of machine-powered pace vehicles 
to help in achieving extraordinary speeds is far 
from new. Drafting off of a railroad car with spe- 
cially designed aerodynamic shields, a rider in 
1896 was able to exceed 60 MPH (96 km/h), a 
then unheard-of speed. Today the record is just 
under 167 MPH (267 km/h). Clearly one must be 
a highly skilled, powerful rider to approach any- 
thing like this speed; but design factors also come 
into play, and not just in the case of the pace 
vehicle. Just as supersonic jets are quite different 
from ordinary planes, super high-speed bicycles 
are not like the average bike; they are designed in 
such a way that they must be moving faster than 
60 MPH before the rider can even pedal. 

SCIENCE □ E EVERYDAY THINGS 



A PROFESSIONAL BICYCLE RACER’S STREAMLINED HEL- 
MET AND CROUCHED POSITION HELP TO IMPROVE AIR- 
FLOW, thus increasing speed. (Photograph by Ronnen 
Eshel/Corbis. Reproduced by permission.) 

With regard to automobiles, as noted earlier, 
aerodynamics has a strong impact on body 
design. For this reason, cars over the years have 
become steadily more streamlined and aerody- 
namic in appearance, a factor that designers bal- 
ance with aesthetic appeal. Today’s Chrysler PT 
Cruiser, which debuted in 2000, may share out- 
ward features with 1930s and 1940s cars, but the 
PT Cruiser’s design is much more sound aerody- 
namically — not least because a modern vehicle 
can travel much, much faster than the cars driv- 
en by previous generations. 

Nowhere does the connection between aero- 
dynamics and automobiles become more crucial 
than in the sport of auto racing. For race-car 
drivers, drag is always a factor to be avoided and 
counteracted by means ranging from drafting to 
altering the body design to reduce the airflow 
under the vehicle. However, as strange as it may 
seem, a car — like an airplane — is also subject to 
lift. 

It was noted earlier that in some cases lift 
can be undesirable in an airplane (for instance, 
when trying to land), but it is virtually always 
undesirable in an automobile. The greater the 
speed, the greater the lift force, which increases 

VDLUME 2: REAL-LIFE PHYSICS 


Aero- 

dynamics 


1 D9 


Aero- 

dynamics 


KEY TERMS 


aerodynamics: The study of air 

flow and its principles. Applied aerody- 
namics is the science of improving man- 
made objects in light of those principles. 

airfoil: The design of an airplane’s 
wing when seen from the end, a shape 
intended to maximize the aircraft’s 
response to airflow. 

angle df attack: The orientation of 
the airfoil with regard to the airflow, or the 
angle that the chord line forms with the 
direction of the air stream. 

Bernoulli’s pri n c i ple: A proposi- 
tion, credited to Swiss mathematician and 
physicist Daniel Bernoulli (1700-1782), 
which maintains that slower-moving fluid 
exerts greater pressure than faster-moving 
fluid. 

camber: The enhanced curvature on the 
upper surface of an airfoil. 

chord line: The distance, along an 
imaginary straight line, from the stagna- 
tion point of an airfoil to the rear, or trail- 
ing edge. 

d rag: The force that opposes the forward 
motion of an object in airflow. 

laminar: A term describing a stream- 
lined flow, in which all particles move at 


the same speed and in the same direction. 
Its opposite is turbulent flow. 

lift: An aerodynamic force perpendicu- 
lar to the direction of the wind. For an air- 
craft, lift is the force that raises it off the 
ground and keeps it aloft. 

pitch: The tendency of an aircraft in 
flight to rotate forward or backward; see 
also yaw and roll. 

roll: The tendency of an aircraft in 
flight to rotate vertically on the axis of its 
fuselage; see also pitch and yaw. 

stae nation paiNT: The spot where 
airflow hits the leading edge of an airfoil. 

supersonic: Faster than Mach 1, or 
the speed of sound — 660 MPF1 (1,622 
km/h). Speeds above Mach 5 are referred to 
as hypersonic. 

turbulent: A term describing a highly 
irregular form of flow, in which a fluid is 
subject to continual changes in speed and 
direction. Its opposite is laminar flow. 

viscosity: The internal friction in a 
fluid that makes it resistant to flow. 

yaw: The tendency of an aircraft in flight 
to rotate on a horizontal plane; see also 
Pitch and Roll. 


| 1 1 □ 


the threat of instability. For this reason, builders 
of race cars design their vehicles for negative lift: 
hence a typical family car has a lift coefficient of 
about 0.03, whereas a race car is likely to have a 
coefficient of -3.00. 

Among the design features most often used 
to reduce drag while achieving negative lift is a 
rear-deck spoiler. The latter has an airfoil shape, 
but its purpose is different: to raise the rear stag- 
nation point and direct air flow so that it does 

vdlume z: real-life physics 


not wrap around the vehicle’s rear end. Instead, 
the spoiler creates a downward force to stabilize 
the rear, and it may help to decrease drag by 
reducing the separation of airflow (and hence the 
creation of turbulence) at the rear window. 

Similar in concept to a spoiler, though some- 
what different in purpose, is the aerodynamically 
curved shield that sits atop the cab of most mod- 
ern eighteen-wheel transport trucks. The pur- 
pose of the shield becomes apparent when the 

SCIENCE DF EVERYDAY THINGS 



truck is moving at high speeds: wind resistance 
becomes strong, and if the wind were to hit the 
truck’s trailer head-on, it would be as though the 
air were pounding a brick wall. Instead, the shield 
scoops air upward, toward the rear of the truck. 
At the rear may be another panel, patented by 
two young engineers in 1994, that creates a drag- 
reducing vortex between panel and truck. 

WHERE TO LEARN M □ R E 

Cockpit Physics (Department of Physics, United States 
Air Force Academy web site.). 

<http://www.usafa.af.mil/dfp/cockpit-phys/> (Febru- 
ary 19, 2001). 

K8AIT Principles of Aeronautics Advanced Text, (web 
site). <http://wings.ucdavis.edu/Book/advanced. 
html> (February 19, 2001). 


Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

Blackburn, Ken. Paper Airplane Aerodynamics, (web site). 
<http://www.geocities.com/CapeCanaveral/1817/ 
paero.html> (February 19, 2001). 

Schrier, Eric and William F. Allman. Newton at the Bat: 
The Science in Sports. New York: Charles Scribner’s 
Sons, 1984. 

Smith, H. C. The Illustrated Guide to Aerodynamics. Blue 
Ridge Summit, PA: Tab Books, 1992. 

Stever, H. Guyford, James J. Haggerty, and the Editors of 
Time-Life Books. Flight. New York: Time-Life Books, 
1965. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 


Aero- 

dynamics 


1 1 1 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


BERNOULLI’S 


PRINCIPLE 


1 1 z 


C □ N C E PT 

Bernoulli’s principle, sometimes known as 
Bernoulli’s equation, holds that for fluids in an 
ideal state, pressure and density are inversely 
related: in other words, a slow-moving fluid 
exerts more pressure than a fast-moving fluid. 
Since “fluid” in this context applies equally to liq- 
uids and gases, the principle has as many appli- 
cations with regard to airflow as to the flow of 
liquids. One of the most dramatic everyday 
examples of Bernoulli’s principle can be found in 
the airplane, which stays aloft due to pressure dif- 
ferences on the surface of its wing; but the truth 
of the principle is also illustrated in something as 
mundane as a shower curtain that billows 
inward. 


H □ W IT WDRKS 

The Swiss mathematician and physicist Daniel 
Bernoulli (1700-1782) discovered the principle 
that bears his name while conducting experi- 
ments concerning an even more fundamental 
concept: the conservation of energy. This is a law 
of physics that holds that a system isolated from 
all outside factors maintains the same total 
amount of energy, though energy transforma- 
tions from one form to another take place. 

For instance, if you were standing at the top 
of a building holding a baseball over the side, the 
ball would have a certain quantity of potential 
energy — the energy that an object possesses by 
virtue of its position. Once the ball is dropped, it 
immediately begins losing potential energy and 
gaining kinetic energy — the energy that an object 
possesses by virtue of its motion. Since the total 
energy must remain constant, potential and 

VDLUME 2: REAL-LIFE PHYSICS 


kinetic energy have an inverse relationship: as the 
value of one variable decreases, that of the other 
increases in exact proportion. 

The ball cannot keep falling forever, losing 
potential energy and gaining kinetic energy. In 
fact, it can never gain an amount of kinetic ener- 
gy greater than the potential energy it possessed 
in the first place. At the moment before the ball 
hits the ground, its kinetic energy is equal to the 
potential energy it possessed at the top of the 
building. Correspondingly, its potential energy is 
zero — the same amount of kinetic energy it pos- 
sessed before it was dropped. 

Then, as the ball hits the ground, the energy 
is dispersed. Most of it goes into the ground, and 
depending on the rigidity of the ball and the 
ground, this energy may cause the ball to bounce. 
Some of the energy may appear in the form of 
sound, produced as the ball hits bottom, and 
some will manifest as heat. The total energy, 
however, will not be lost: it will simply have 
changed form. 

Bernoulli was one of the first scientists to 
propose what is known as the kinetic theory of 
gases: that gas, like all matter, is composed of tiny 
molecules in constant motion. In the 1730s, he 
conducted experiments in the conservation of 
energy using liquids, observing how water flows 
through pipes of varying diameter. In a segment 
of pipe with a relatively large diameter, he 
observed, water flowed slowly, but as it entered a 
segment of smaller diameter, its speed increased. 

It was clear that some force had to be acting 
on the water to increase its speed. Earlier, Robert 
Boyle (1627-1691) had demonstrated that pres- 
sure and volume have an inverse relationship, 

SCIENCE □ F EVERYDAY THINGS 



and Bernoulli seems to have applied Boyle’s find- 
ings to the present situation. Clearly the volume 
of water flowing through the narrower pipe at 
any given moment was less than that flowing 
through the wider one. This suggested, according 
to Boyle’s law, that the pressure in the wider pipe 
must be greater. 

As fluid moves from a wider pipe to a nar- 
rower one, the volume of that fluid that moves a 
given distance in a given time period does not 
change. But since the width of the narrower pipe 
is smaller, the fluid must move faster in order to 
achieve that result. One way to illustrate this is to 
observe the behavior of a river: in a wide, uncon- 
stricted region, it flows slowly, but if its flow is 
narrowed by canyon walls (for instance), then it 
speeds up dramatically. 

The above is a result of the fact that water is 
a fluid, and having the characteristics of a fluid, it 
adjusts its shape to fit that of its container or 
other solid objects it encounters on its path. 
Since the volume passing through a given length 
of pipe during a given period of time will be the 
same, there must be a decrease in pressure. Hence 
Bernoulli’s conclusion: the slower the rate of 
flow, the higher the pressure, and the faster the 
rate of flow, the lower the pressure. 

Bernoulli published the results of his work 
in Hydrodynamica (1738), but did not present his 
ideas or their implications clearly. Later, his 
friend the German mathematician Leonhard 
Euler (1707-1783) generalized his findings 
in the statement known today as Bernoulli’s 
principle. 

The Venturi Tube 

Also significant was the work of the Italian physi- 
cist Giovanni Venturi (1746-1822), who is credit- 
ed with developing the Venturi tube, an instru- 
ment for measuring the drop in pressure that 
takes place as the velocity of a fluid increases. It 
consists of a glass tube with an inward-sloping 
area in the middle, and manometers, devices for 
measuring pressure, at three places: the entrance, 
the point of constriction, and the exit. The Ven- 
turi meter provided a consistent means of 
demonstrating Bernoulli’s principle. 

Like many propositions in physics, 
Bernoulli’s principle describes an ideal situation 
in the absence of other forces. One such force is 


viscosity, the internal friction in a fluid that 
makes it resistant to flow. In 1904, the German 
physicist Ludwig Prandtl (1875-1953) was con- 
ducting experiments in liquid flow, the first 
effort in well over a century to advance the find- 
ings of Bernoulli and others. Observing the flow 
of liquid in a tube, Prandtl found that a tiny 
portion of the liquid adheres to the surface of 
the tube in the form of a thin film, and does not 
continue to move. This he called the viscous 
boundary layer. 

Like Bernoulli’s principle itself, Prandtl’s 
findings would play a significant part in aerody- 
namics, or the study of airflow and its principles. 
They are also significant in hydrodynamics, or 
the study of water flow and its principles, a disci- 
pline Bernoulli founded. 

Laminar vs. Turbulent Flow 

Air and water are both examples of fluids, sub- 
stances which — whether gas or liquid — conform 
to the shape of their container. The flow patterns 
of all fluids may be described in terms either of 
laminar flow, or of its opposite, turbulent flow. 

Laminar flow is smooth and regular, always 
moving at the same speed and in the same direc- 
tion. Also known as streamlined flow, it is char- 
acterized by a situation in which every particle of 
fluid that passes a particular point follows a path 
identical to all particles that passed that point 
earlier. A good illustration of laminar flow is 
what occurs when a stream flows around a twig. 

By contrast, in turbulent flow, the fluid is 
subject to continual changes in speed and direc- 
tion — as, for instance, when a stream flows over 
shoals of rocks. Whereas the mathematical model 
of laminar flow is rather straightforward, condi- 
tions are much more complex in turbulent flow, 
which typically occurs in the presence of obsta- 
cles or high speeds. 

Turbulent flow makes it more difficult for 
two streams of air, separated after hitting a barri- 
er, to rejoin on the other side of the barrier; yet 
that is their natural tendency. In fact, if a single 
air current hits an airfoil — the design of an air- 
plane’s wing when seen from the end, a stream- 
lined shape intended to maximize the aircraft’s 
response to airflow — the air that flows over the 
top will “try” to reach the back end of the airfoil 
at the same time as the air that flows over the 


Bernoulli's 

Principle 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 1 3 



A kite’s design, particularly its use of lightweight fabric stretched over two crossed strips of very 

LIGHT WOOD, MAKES IT WELL-SUITED FOR FLIGHT, BUT WHAT KEEPS IT IN THE AIR IS A DIFFERENCE IN AIR PRESSURE. 
At THE BEST POSSIBLE ANGLE OF ATTACK, THE KITE EXPERIENCES AN IDEAL RATIO OF PRESSURE FROM THE SLOW- 
ER-MOVING air below versus the faster-moving air ABOVE, and this gives it lift. (Roger Ressmeyer/Corbis. Repro- 
duced by permission.) 


bottom. In order to do so, it will need to speed 
up — and this, as will be shown below, is the basis 
for what makes an airplane fly. 


When viscosity is absent, conditions of per- 
fect laminar flow exist: an object behaves in com- 
plete alignment with Bernoulli’s principle. Of 


| 1 1 4 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 




The boomerang, developed by Australia’s Aboriginal people, flies through the air on a plane per- 
pendicular TO THE GROUND, RATHER THAN PARALLEL. As IT FLIES, THE BOOMERANG BECOMES BOTH A GYROSCOPE 

and an airfoil, and this dual role gives it aerodynamic lift. (Bettmann/Corbis. Reproduced by permission.) 


course, though ideal conditions seldom occur in 
the real world, Bernoulli’s principle provides a 
guide for the behavior of planes in flight, as well 
as a host of everyday things. 

REAL-LIFE 
A P P L I C AT I □ N S 

Flying Machines 

For thousands of years, human beings vainly 
sought to fly “like a bird,” not realizing that this is 
literally impossible, due to differences in phys- 
iognomy between birds and homo sapiens. No 
man has ever been born (or ever will be) who 
possesses enough strength in his chest that he 
could flap a set of attached wings and lift his 
body off the ground. Yet the bird’s physical struc- 
ture proved highly useful to designers of practi- 
cal flying machines. 

A bird’s wing is curved along the top, so that 
when air passes over the wing and divides, the 
curve forces the air on top to travel a greater dis- 
tance than the air on the bottom. The tendency 
of airflow, as noted earlier, is to correct for the 
presence of solid objects and to return to its orig- 
inal pattern as quickly as possible. Hence, when 

SCIENCE □ E EVERYDAY THINGS 


the air hits the front of the wing, the rate of flow 
at the top increases to compensate for the greater 
distance it has to travel than the air below the 
wing. And as shown by Bernoulli, fast-moving 
fluid exerts less pressure than slow-moving fluid; 
therefore, there is a difference in pressure 
between the air below and the air above, and this 
keeps the wing aloft. 

Only in 1853 did Sir George Cayley (1773- 
1857) incorporate the avian airfoil to create his- 
tory’s first workable (though engine-less) flying 
machine, a glider. Much, much older than Cay- 
ley’s glider, however, was the first manmade fly- 
ing machine built “according to Bernoulli’s prin- 
ciple” — only it first appeared in about 12,000 
b.c., and the people who created it had had little 
contact with the outside world until the late eigh- 
teenth century a.d. This was the boomerang, one 
of the most ingenious devices ever created by a 
stone-age society — in this case, the Aborigines of 
Australia. 

Contrary to the popular image, a 
boomerang flies through the air on a plane per- 
pendicular to the ground, rather than parallel. 
Hence, any thrower who properly knows how 
tosses the boomerang not with a side-arm throw, 
but overhand. As it flies, the boomerang becomes 

VDLUME 2: REAL-LIFE PHYSICS 


1 1 5 


Bernoulli’s 

Principle 


both a gyroscope and an airfoil, and this dual role 
gives it aerodynamic lift. 

Like the gyroscope, the boomerang imitates 
a top; spinning keeps it stable. It spins through 
the air, its leading wing (the forward or upward 
wing) creating more lift than the other wing. As 
an airfoil, the boomerang is designed so that the 
air below exerts more pressure than the air above, 
which keeps it airborne. 

Another very early example of a flying 
machine using Bernoulli’s principles is the kite, 
which first appeared in China in about 1000 b.c. 
The kite’s design, particularly its use of light- 
weight fabric stretched over two crossed strips of 
very light wood, makes it well-suited for flight, 
but what keeps it in the air is a difference in air 
pressure. At the best possible angle of attack, the 
kite experiences an ideal ratio of pressure from 
the slower-moving air below versus the faster- 
moving air above, and this gives it lift. 

Later Cayley studied the operation of the 
kite, and recognized that it — rather than the bal- 
loon, which at first seemed the most promising 
apparatus for flight — was an appropriate model 
for the type of heavier-than-air flying machine 
he intended to build. Due to the lack of a motor, 
however, Cayley’s prototypical airplane could 
never be more than a glider: a steam engine, then 
state-of-the-art technology, would have been 
much too heavy. 

Hence, it was only with the invention of the 
internal-combustion engine that the modern air- 
plane came into being. On December 17, 1903, at 
Kitty Hawk, North Carolina, Orville (1871-1948) 
and Wilbur (1867-1912) Wright tested a craft 
that used a 25-horsepower engine they had 
developed at their bicycle shop in Ohio. By max- 
imizing the ratio of power to weight, the engine 
helped them overcome the obstacles that had 
dogged recent attempts at flight, and by the time 
the day was over, they had achieved a dream that 
had eluded men for more than four millennia. 

Within fifty years, airplanes would increas- 
ingly obtain their power from jet rather than 
internal-combustion engines. But the principle 
that gave them flight, and the principle that kept 
them aloft once they were airborne, reflected 
back to Bernoulli’s findings of more than 160 
years before their time. This is the concept of the 
airfoil. 

As noted earlier, an airfoil has a streamlined 
design. Its shape is rather like that of an elongat- 


ed, asymmetrical teardrop lying on its side, with 
the large end toward the direction of airflow, and 
the narrow tip pointing toward the rear. The 
greater curvature of its upper surface in compar- 
ison to the lower side is referred to as the air- 
plane’s camber. The front end of the airfoil is also 
curved, and the chord line is an imaginary 
straight line connecting the spot where the air 
hits the front — known as the stagnation point — 
to the rear, or trailing edge, of the wing. 

Again, in accordance with Bernoulli’s princi- 
ple, the shape of the airflow facilitates the spread 
of laminar flow around it. The slower-moving 
currents beneath the airfoil exert greater pressure 
than the faster currents above it, giving lift to the 
aircraft. Of course, the aircraft has to be moving 
at speeds sufficient to gain momentum for its 
leap from the ground into the air, and here again, 
Bernoulli’s principle plays a part. 

Thrust comes from the engines, which run 
the propellers — whose blades in turn are 
designed as miniature airfoils to maximize their 
power by harnessing airflow. Like the aircraft 
wings, the blades’ angle of attack — the angle at 
which airflow hits it. In stable flight, the pilot 
greatly increases the angle of attack (also called 
pitched), whereas at takeoff and landing, the 
pitch is dramatically reduced. 

Drawing Fluids Upward: 
Atomizers and Chimneys 

A number of everyday objects use Bernoulli’s 
principle to draw fluids upward, and though in 
terms of their purposes, they might seem very 
different — for instance, a perfume atomizer vs. a 
chimney — they are closely related in their appli- 
cation of pressure differences. In fact, the idea 
behind an atomizer for a perfume spray bottle 
can also be found in certain garden-hose attach- 
ments, such as those used to provide a high-pres- 
sure car wash. 

The air inside the perfume bottle is moving 
relatively slowly; therefore, according to Bernoul- 
li’s principle, its pressure is relatively high, and it 
exerts a strong downward force on the perfume 
itself. In an atomizer there is a narrow tube run- 
ning from near the bottom of the bottle to the 
top. At the top of the perfume bottle, it opens 
inside another tube, this one perpendicular to 
the first tube. At one end of the horizontal tube is 
a simple squeeze-pump which causes air to flow 
quickly through it. As a result, the pressure 


1 1 6 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


toward the top of the bottle is reduced, and the 
perfume flows upward along the vertical tube, 
drawn from the area of higher pressure at the 
bottom. Once it is in the upper tube, the squeeze- 
pump helps to eject it from the spray nozzle. 

A carburetor works on a similar principle, 
though in that case the lower pressure at the top 
draws air rather than liquid. Likewise a chimney 
draws air upward, and this explains why a windy 
day outside makes for a better fire inside. With 
wind blowing over the top of the chimney, the air 
pressure at the top is reduced, and tends to draw 
higher-pressure air from down below. 

The upward pull of air according to the 
Bernoulli principle can also be illustrated by 
what is sometimes called the “Hoover bugle” — a 
name perhaps dating from the Great Depression, 
when anything cheap or contrived bore the 
appellation “Hoover” as a reflection of popular 
dissatisfaction with President Herbert Hoover. In 
any case, the Hoover bugle is simply a long cor- 
rugated tube that, when swung overhead, pro- 
duces musical notes. 

You can create a Hoover bugle using any sort 
of corrugated tube, such as vacuum-cleaner hose 
or swimming-pool drain hose, about 1.8 in (4 
cm) in diameter and 6 ft (1.8 m) in length. To 
operate it, you should simply hold the tube in 
both hands, with extra length in the leading 
hand — that is, the right hand, for most people. 
This is the hand with which to swing the tube 
over your head, first slowly and then faster, 
observing the changes in tone that occur as you 
change the pace. 

The vacuum hose of a Hoover tube can also 
be returned to a version of its original purpose in 
an illustration of Bernoulli’s principle. If a piece 
of paper is torn into pieces and placed on a table, 
with one end of the tube just above the paper and 
the other end spinning in the air, the paper tends 
to rise. It is drawn upward as though by a vacu- 
um cleaner — but in fact, what makes it happen is 
the pressure difference created by the movement 
of air. 

In both cases, reduced pressure draws air 
from the slow-moving region at the bottom of 
the tube. In the case of the Hoover bugle, the cor- 
rugations produce oscillations of a certain fre- 
quency. Slower speeds result in slower oscilla- 
tions and hence lower frequency, which produces 
a lower tone. At higher speeds, the opposite is 


true. There is little variation in tones on a Hoover 
bugle: increasing the velocity results in a fre- 
quency twice that of the original, but it is difficult 
to create enough speed to generate a third tone. 

Spin, Curve, and Pull: The 
Counterintuitive Principle 

There are several other interesting illustrations — 
sometimes fun and in one case potentially trag- 
ic — of Bernoulli’s principle. For instance, there is 
the reason why a shower curtain billows inward 
once the shower is turned on. It would seem log- 
ical at first that the pressure created by the water 
would push the curtain outward, securing it to 
the side of the bathtub. 

Instead, of course, the fast-moving air gener- 
ated by the flow of water from the shower creates 
a center of lower pressure, and this causes the 
curtain to move away from the slower-moving 
air outside. This is just one example of the ways 
in which Bernoulli’s principle creates results that, 
on first glance at least, seem counterintuitive — 
that is, the opposite of what common sense 
would dictate. 

Another fascinating illustration involves 
placing two empty soft drink cans parallel to one 
another on a table, with a couple of inches or a 
few centimeters between them. At that point, the 
air on all sides has the same slow speed. If you 
were to blow directly between the cans, however, 
this would create an area of low pressure between 
them. As a result, the cans push together. For 
ships in a harbor, this can be a frightening 
prospect: hence, if two crafts are parallel to one 
another and a strong wind blows between them, 
there is a possibility that they may behave like the 
cans. 

Then there is one of the most illusory uses of 
Bernoulli’s principle, that infamous baseball 
pitcher’s trick called the curve ball. As the ball 
moves through the air toward the plate, its veloc- 
ity creates an air stream moving against the tra- 
jectory of the ball itself. Imagine it as two lines, 
one curving over the ball and one curving under, 
as the ball moves in the opposite direction. 

In an ordinary throw, the effects of the air- 
flow would not be particularly intriguing, but in 
this case, the pitcher has deliberately placed a 
“spin” on the ball by the manner in which he has 
thrown it. How pitchers actually produce spin is 
a complex subject unto itself, involving grip, 


Bernoulli’s 

Principle 


SCIENCE □ E EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


1 1 7 


Bernoulli’s 

Principle 


KEY TERMS 


aerodynamics: The study of air- 

flow and its principles. Applied aerody- 
namics is the science of improving man- 
made objects in light of those principles. 

airfdil: The design of an airplane’s 

wing when seen from the end, a shape 
intended to maximize the aircraft’s 
response to airflow. 

angle of attack: The orientation of 
the airfoil with regard to the airflow, or the 
angle that the chord line forms with the 
direction of the air stream. 

Bernoulli's pri n c i ple: A proposi- 
tion, credited to Swiss mathematician and 
physicist Daniel Bernoulli (1700-1782), 
which maintains that slower-moving fluid 
exerts greater pressure than faster-moving 
fluid. 

camber: The enhanced curvature on the 
upper surface of an airfoil. 

chord line: The distance, along an 
imaginary straight line, from the stagna- 
tion point of an airfoil to the rear, or trail- 
ing edge. 

CONSERVATION OF ENERGY: A 

law of physics which holds that within a 
system isolated from all other outside fac- 
tors, the total amount of energy remains 
the same, though transformations of ener- 
gy from one form to another take place. 

fluid: Any substance, whether gas or 

liquid, that conforms to the shape of its 
container. 

hydrodynamics: The study of 

water flow and its principles. 


inverse relationship: A situa- 

tion involving two variables, in which one 
of the two increases in direct proportion to 
the decrease in the other. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 

laminar: A term describing a stream- 
lined flow, in which all particles move at 
the same speed and in the same direction. 
Its opposite is turbulent flow. 

lift: An aerodynamic force perpendicu- 
lar to the direction of the wind. For an air- 
craft, lift is the force that raises it off the 
ground and keeps it aloft. 

manometers: Devices for measur- 

ing pressure in conjunction with a Venturi 
tube. 

potential energy: The energy 

that an object possesses by virtue of its 
position. stag n ati □ n point: The spot 
where airflow hits the leading edge of an 
airfoil. 

turbulent: A term describing a highly 
irregular form of flow, in which a fluid is 
subject to continual changes in speed and 
direction. Its opposite is laminar flow. 

venturi tube: An instrument, con- 

sisting of a glass tube with an inward-slop- 
ing area in the middle, for measuring the 
drop in pressure that takes place as the 
velocity of a fluid increases. 

viscosity: The internal friction in a 
fluid that makes it resistant to flow. 


wrist movement, and other factors, and in any If the direction of airflow is from right to 

case, the fact of the spin is more important than left, the ball, as it moves into the airflow, is spin- 

the way in which it was achieved. ning clockwise. This means that the air flowing 


1 1 B 


VOLUME 2: real-life physics 


SCIENCE OF EVERYDAY THINGS 



over the ball is moving in a direction opposite to 
the spin, whereas that flowing under it is moving 
in the same direction. The opposite forces pro- 
duce a drag on the top of the ball, and this cuts 
down on the velocity at the top compared to that 
at the bottom of the ball, where spin and airflow 
are moving in the same direction. 

Thus the air pressure is higher at the top of 
the ball, and as per Bernoulli’s principle, this 
tends to pull the ball downward. The curve ball — 
of which there are numerous variations, such as 
the fade and the slider — creates an unpredictable 
situation for the batter, who sees the ball leave the 
pitcher’s hand at one altitude, but finds to his dis- 
may that it has dropped dramatically by the time 
it crosses the plate. 

A final illustration of Bernoulli’s often coun- 
terintuitive principle neatly sums up its effects on 
the behavior of objects. To perform the experi- 
ment, you need only an index card and a flat sur- 
face. The index card should be folded at the ends 
so that when the card is parallel to the surface, 
the ends are perpendicular to it. These folds 
should be placed about half an inch (about one 
centimeter) from the ends. 

At this point, it would be handy to have an 
unsuspecting person — someone who has not 
studied Bernoulli’s principle — on the scene, and 
challenge him or her to raise the card by blowing 
under it. Nothing could seem easier, of course: by 


blowing under the card, any person would natu- 
rally assume, the air will lift it. But of course this 
is completely wrong according to Bernoulli’s 
principle. Blowing under the card, as illustrated, 
will create an area of high velocity and low pres- 
sure. This will do nothing to lift the card: in fact, 
it only pushes the card more firmly down on the 
table. 

WHERE TD LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Bernoulli’s Principle: Explanations and Demos.” (Web 
site), <http://207.10.97.102/physicszone/lesson/ 
02forces/bernoull/bernoul l.html> (February 22, 
2001 ). 

Cockpit Physics (Department of Physics, United States 
Air Force Academy. Web site.). 

<http://www.usafa.af.mil/dfp/cockpit-phys/> (Febru- 
ary 19, 2001). 

K8AIT Principles of Aeronautics Advanced Text. (Web 
site). <http://wings.ucdavis.edu/Book/advanced. 
html> (February 19, 2001). 

Schrier, Eric and William F. Allman. Newton at the Bat: 
The Science in Sports. New York: Charles Scribner’s 
Sons, 1984. 

Smith, H. C. The Illustrated Guide to Aerodynamics. Blue 
Ridge Summit, PA: Tab Books, 1992. 

Stever, H. Guyford, James J. Haggerty, and the Editors of 
Time-Life Books. Flight. New York: Time-Life Books, 
1965. 


Bernoulli’s 

Principle 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 1 9 


BUD YA N C Y 


C □ N C E PT 

The principle of buoyancy holds that the buoy- 
ant or lifting force of an object submerged in a 
fluid is equal to the weight of the fluid it has dis- 
placed. The concept is also known as 
Archimedes’s principle, after the Greek mathe- 
matician, physicist, and inventor Archimedes (c. 
287-212 b.c.), who discovered it. Applications of 
Archimedes’s principle can be seen across a wide 
vertical spectrum: from objects deep beneath the 
oceans to those floating on its surface, and from 
the surface to the upper limits of the stratosphere 
and beyond. 

H □ W IT WDRKS 

Archimedes Discovers Buoy- 
ancy 

There is a famous story that Sir Isaac Newton 
(1642-1727) discovered the principle of gravity 
when an apple fell on his head. The tale, an exag- 
gerated version of real events, has become so 
much a part of popular culture that it has been 
parodied in television commercials. Almost 
equally well known is the legend of how 
Archimedes discovered the concept of buoyancy. 

A native of Syracuse, a Greek colony in Sici- 
ly, Archimedes was related to one of that city’s 
kings, Hiero II (308?-216 B.C.). After studying in 
Alexandria, Egypt, he returned to his hometown, 
where he spent the remainder of his life. At some 
point, the royal court hired (or compelled) him 
to set about determining the weight of the gold 
in the king’s crown. Archimedes was in his bath 
pondering this challenge when suddenly it 
occurred to him that the buoyant force of a sub- 

VDLUME 2: REAL-LIFE PHYSICS 


merged object is equal to the weight of the fluid 
displaced by it. 

He was so excited, the legend goes, that he 
jumped out of his bath and ran naked through 
the streets of Syracuse shouting “Eureka!” (I have 
found it). Archimedes had recognized a principle 
of enormous value — as will be shown — to ship- 
builders in his time, and indeed to shipbuilders 
of the present. 

Concerning the history of science, it was a 
particularly significant discovery; few useful and 
enduring principles of physics date to the period 
before Galileo Galilei (1564-1642.) Even among 
those few ancient physicists and inventors who 
contributed work of lasting value — Archimedes, 
Hero of Alexandria (c. 65-125 A.D.), and a few 
others — there was a tendency to miss the larger 
implications of their work. For example, Hero, 
who discovered steam power, considered it useful 
only as a toy, and as a result, this enormously sig- 
nificant discovery was ignored for seventeen cen- 
turies. 

In the case of Archimedes and buoyancy, 
however, the practical implications of the discov- 
ery were more obvious. Whereas steam power 
must indeed have seemed like a fanciful notion to 
the ancients, there was nothing farfetched about 
oceangoing vessels. Shipbuilders had long been 
confronted with the problem of how to keep a 
vessel afloat by controlling the size of its load on 
the one hand, and on the other hand, its tenden- 
cy to bob above the water. Here, Archimedes 
offered an answer. 

Buoyancy and Weight 

Why does an object seem to weigh less underwa- 
ter than above the surface? How is it that a ship 

SCIENCE □ F EVERYDAY THINGS 



Buoyancy 


made of steel, which is obviously heavier than 
water, can float? How can we determine whether 
a balloon will ascend in the air, or a submarine 
will descend in the water? These and other ques- 
tions are addressed by the principle of buoyancy, 
which can be explained in terms of properties — 
most notably, gravity — unknown to Archimedes. 

To understand the factors at work, it is use- 
ful to begin with a thought experiment. Imagine 
a certain quantity of fluid submerged within a 
larger body of the same fluid. Note that the terms 
“liquid” or “water” have not been used: not only 
is “fluid” a much more general term, but also, in 
general physical terms and for the purposes of 
the present discussion, there is no significant dif- 
ference between gases and liquids. Both conform 
to the shape of the container in which they are 
placed, and thus both are fluids. 

To return to the thought experiment, what 
has been posited is in effect a “bag” of fluid — that 
is, a “bag” made out of fluid and containing fluid 
no different from the substance outside the 
“bag.” This “bag” is subjected to a number of 
forces. First of all, there is its weight, which tends 
to pull it to the bottom of the container. There is 
also the pressure of the fluid all around it, which 
varies with depth: the deeper within the contain- 
er, the greater the pressure. 

Pressure is simply the exertion of force over 
a two-dimensional area. Thus it is as though the 
fluid is composed of a huge number of two- 
dimensional “sheets” of fluid, each on top of the 
other, like pages in a newspaper. The deeper into 
the larger body of fluid one goes, the greater the 
pressure; yet it is precisely this increased force at 
the bottom of the fluid that tends to push the 
“bag” upward, against the force of gravity. 

Now consider the weight of this “bag.” 
Weight is a force — the product of mass multi- 
plied by acceleration — that is, the downward 
acceleration due to Earth’s gravitational pull. For 
an object suspended in fluid, it is useful to sub- 
stitute another term for mass. Mass is equal to 
volume, or the amount of three-dimensional 
space occupied by an object, multiplied by densi- 
ty. Since density is equal to mass divided by vol- 
ume, this means that volume multiplied by den- 
sity is the same as mass. 

We have established that the weight of the 
fluid “bag” is Vdg, where V is volume, d is densi- 
ty, and g is the acceleration due to gravity. Now 
imagine that the “bag” has been replaced by a 

SCIENCE □ E EVERYDAY THINGS 


solid object of exactly the same size. The solid 
object will experience exactly the same degree of 
pressure as the imaginary “bag” did — and hence, 
it will also experience the same buoyant force 
pushing it up from the bottom. This means that 
buoyant force is equal to the weight — Vdg — of 
displaced fluid. 

Buoyancy is always a double-edged proposi- 
tion. If the buoyant force on an object is greater 
than the weight of that object — in other words, if 
the object weighs less than the amount of water 
it has displaced — it will float. But if the buoyant 
force is less than the object’s weight, the object 
will sink. Buoyant force is not the same as net 
force: if the object weighs more than the water it 
displaces, the force of its weight cancels out and 
in fact “overrules” that of the buoyant force. 

At the heart of the issue is density. Often, the 
density of an object in relation to water is 
referred to as its specific gravity: most metals, 
which are heavier than water, are said to have a 
high specific gravity. Conversely, petroleum- 
based products typically float on the surface of 
water, because their specific gravity is low. Note 
the close relationship between density and 
weight where buoyancy is concerned: in fact, the 
most buoyant objects are those with a relatively 
high volume and a relatively low density. 

This can be shown mathematically by means 
of the formula noted earlier, whereby density is 
equal to mass divided by volume. If Vd = 
V(m/V), an increase in density can only mean an 
increase in mass. Since weight is the product of 
mass multiplied by g (which is assumed to be a 
constant figure), then an increase in density 
means an increase in mass and hence, an increase 
in weight — not a good thing if one wants an 
object to float. 

R E A L- L I F E 
A P P L I C AT I □ N S 

Staying Afloat 

In the early 1800s, a young Mississippi River flat- 
boat operator submitted a patent application 
describing a device for “buoying vessels over 
shoals.” The invention proposed to prevent a 
problem he had often witnessed on the river — 
boats grounded on sandbars — by equipping the 
boats with adjustable buoyant air chambers. The 
young man even whittled a model of his inven- 

VDLUME 2: REAL-LIFE PHYSICS 


1 2 1 


BUDYANCY 


| 1 2Z 


tion, but he was not destined for fame as an 
inventor; instead, Abraham Lincoln (1809-1865) 
was famous for much else. In fact Lincoln had a 
sound idea with his proposal to use buoyant 
force in protecting boats from running aground. 

Buoyancy on the surface of water has a num- 
ber of easily noticeable effects in the real world. 
(Having established the definition of fluid, from 
this point onward, the fluids discussed will be 
primarily those most commonly experienced: 
water and air.) It is due to buoyancy that fish, 
human swimmers, icebergs, and ships stay afloat. 
Fish offer an interesting application of volume 
change as a means of altering buoyancy: a fish 
has an internal swim bladder, which is filled with 
gas. When it needs to rise or descend, it changes 
the volume in its swim bladder, which then 
changes its density. The examples of swimmers 
and icebergs directly illustrate the principle of 
density — on the part of the water in the first 
instance, and on the part of the object itself in the 
second. 

To a swimmer, the difference between swim- 
ming in fresh water and salt water shows that 
buoyant force depends as much on the density of 
the fluid as on the volume displaced. Fresh water 
has a density of 62.4 lb/ft 3 (9,925 N/m 3 ), whereas 
that of salt water is 64 lb/ft 3 (10,167 N/m 3 ). For 
this reason, salt water provides more buoyant 
force than fresh water; in Israel’s Dead Sea, the 
saltiest body of water on Earth, bathers experi- 
ence an enormous amount of buoyant force. 

Water is an unusual substance in a number 
of regards, not least its behavior as it freezes. 
Close to the freezing point, water thickens up, 
but once it turns to ice, it becomes less dense. 
This is why ice cubes and icebergs float. Howev- 
er, their low density in comparison to the water 
around them means that only part of an iceberg 
stays atop the surface. The submerged percentage 
of an iceberg is the same as the ratio of the den- 
sity of ice to that of water: 89%. 

Ships at Sea 

Because water itself is relatively dense, a high- 
volume, low-density object is likely to displace a 
quantity of water more dense — and heavier — 
than the object itself. By contrast, a steel ball 
dropped into the water will sink straight to the 
bottom, because it is a low-volume, high-density 
object that outweighs the water it displaced. 

VDLUME 2: REAL-LIFE PHYSICS 


This brings back the earlier question: how 
can a ship made out of steel, with a density of 487 
lb/ft 3 (77,363 N/m 3 ), float on a salt-water ocean 
with an average density of only about one-eighth 
that amount? The answer lies in the design of the 
ship’s hull. If the ship were flat like a raff, or if all 
the steel in it were compressed into a ball, it 
would indeed sink. Instead, however, the hollow 
hull displaces a volume of water heavier than the 
ship’s own weight: once again, volume has been 
maximized, and density minimized. 

For a ship to be seaworthy, it must maintain 
a delicate balance between buoyancy and stabili- 
ty. A vessel that is too light — that is, too much 
volume and too little density — will bob on the 
top of the water. Therefore, it needs to carry a 
certain amount of cargo, and if not cargo, then 
water or some other form of ballast. Ballast is a 
heavy substance that increases the weight of an 
object experiencing buoyancy, and thereby 
improves its stability. 

Ideally, the ship’s center of gravity should be 
vertically aligned with its center of buoyancy. The 
center of gravity is the geometric center of the 
ship’s weight — the point at which weight above is 
equal to weight below, weight fore is equal to 
weight aft, and starboard (right-side) weight is 
equal to weight on the port (left) side. The center 
of buoyancy is the geometric center of its sub- 
merged volume, and in a stable ship, it is some 
distance directly below center of gravity. 

Displacement, or the weight of the fluid that 
is moved out of position when an object is 
immersed, gives some idea of a ship’s stability. If 
a ship set down in the ocean causes 1,000 tons 
(8.896 • 10 6 N) of water to be displaced, it is said 
to possess a displacement of 1,000 tons. Obvi- 
ously, a high degree of displacement is desirable. 
The principle of displacement helps to explain 
how an aircraft carrier can remain afloat, even 
though it weighs many thousands of tons. 

Down to the Depths 

A submarine uses ballast as a means of descend- 
ing and ascending underwater: when the subma- 
rine captain orders the crew to take the craft 
down, the craft is allowed to take water into its 
ballast tanks. If, on the other hand, the command 
is given to rise toward the surface, a valve will be 
opened to release compressed air into the tanks. 
The air pushes out the water, and causes the craft 
to ascend. 

SCIENCE OF EVERYDAY THINGS 


Buoyancy 



The molecular structure of water begins td expand once it cools beyond 39.4°F (4°C) and continues 

TO EXPAND UNTIL IT BECOMES ICE. FOR THIS REASON, ICE IS LESS DENSE THAN WATER, FLOATS ON THE SURFACE, 
AND RETARDS FURTHER COOLING OF DEEPER WATER, WHICH ACCOUNTS FOR THE SURVIVAL OF FRESHWATER PLANT 
AND ANIMAL LIFE THROUGH THE WINTER. FOR THEIR PART, FISH CHANGE THE VOLUME OF THEIR INTERNAL SWIM BLAD- 
DER IN ORDER TO ALTER THEIR BUOYANCY. 


A submarine is an underwater ship; its 
streamlined shape is designed to ease its move- 
ment. On the other hand, there are certain kinds 
of underwater vessels, known as submersibles, 
that are designed to sink — in order to observe or 
collect data from the ocean floor. Originally, the 
idea of a submersible was closely linked to that of 
diving itself. An early submersible was the diving 
bell, a device created by the noted English 
astronomer Edmund Halley (1656-1742.) 

Though his diving bell made it possible for 
Halley to set up a company in which hired divers 
salvaged wrecks, it did not permit divers to go 
beyond relatively shallow depths. First of all, the 
diving bell received air from the surface: in Hal- 
ley’s time, no technology existed for taking an 
oxygen supply below. Nor did it provide substan- 
tial protection from the effects of increased pres- 
sure at great depths. 

PERILS OF THE DEEP. The mOSt 

immediate of those effects is, of course, the ten- 
dency of an object experiencing such pressure to 
simply implode like a tin can in a vise. Further- 
more, the human body experiences several severe 
reactions to great depth: under water, nitrogen 
gas accumulates in a diver’s bodily tissues, pro- 

SCIENCE DF EVERYDAY THINGS 


ducing two different — but equally frightening — 
effects. 

Nitrogen is an inert gas under normal con- 
ditions, yet in the high pressure of the ocean 
depths it turns into a powerful narcotic, causing 
nitrogen narcosis — often known by the poetic- 
sounding name “rapture of the deep.” Under the 
influence of this deadly euphoria, divers begin to 
think themselves invincible, and their altered 
judgment can put them into potentially fatal sit- 
uations. 

Nitrogen narcosis can occur at depths as 
shallow as 60 ft (18.29 m), and it can be over- 
come simply by returning to the surface. Howev- 
er, one should not return to the surface too 
quickly, particularly after having gone down to a 
significant depth for a substantial period of time. 
In such an instance, on returning to the surface 
nitrogen gas will bubble within the body, pro- 
ducing decompression sickness — known collo- 
quially as “the bends.” This condition may mani- 
fest as itching and other skin problems, joint 
pain, choking, blindness, seizures, unconscious- 
ness, and even permanent neurological defects 
such as paraplegia. 

VDLUME 2: REAL-LIFE PHYSICS 


1 23 


BUDYANCY 


| 1 24 


French physiologist Paul Bert (1833-1886) 
first identified the bends in 1878, and in 1907, 
John Scott Haldane (1860-1936) developed a 
method for counteracting decompression sick- 
ness. He calculated a set of decompression tables 
that advised limits for the amount of time at 
given depths. He recommended what he called 
stage decompression, which means that the 
ascending diver stops every few feet during 
ascension and waits for a few minutes at each 
level, allowing the body tissues time to adjust to 
the new pressure. Modern divers use a decom- 
pression chamber, a sealed container that simu- 
lates the stages of decompression. 

BATHYSPHERE, SCUBA, AND 

bathyscaphe. In 1930, the American 
naturalist William Beebe (1877-1962) and Amer- 
ican engineer Otis Barton created the bathy- 
sphere. This was the first submersible that pro- 
vided the divers inside with adequate protection 
from external pressure. Made of steel and spher- 
ical in shape, the bathysphere had thick quartz 
windows and was capable of maintaining ordi- 
nary atmosphere pressure even when lowered by 
a cable to relatively great depths. In 1934, a bath- 
ysphere descended to what was then an extreme- 
ly impressive depth: 3,028 ft (923 m). However, 
the bathysphere was difficult to operate and 
maneuver, and in time it was be replaced by a 
more workable vessel, the bathyscaphe. 

Before the bathyscaphe appeared, however, 
in 1943, two Frenchmen created a means for 
divers to descend without the need for any sort of 
external chamber. Certainly a diver with this new 
apparatus could not go to anywhere near the 
same depths as those approached by the bathy- 
sphere; nonetheless, the new aqualung made it 
possible to spend an extended time under the 
surface without need for air. It was now theoret- 
ically feasible for a diver to go below without any 
need for help or supplies from above, because he 
carried his entire oxygen supply on his back. The 
name of one of inventors, Emile Gagnan, is hard- 
ly a household word; but that of the other — 
Jacques Cousteau (1910-1997) — certainly is. So, 
too, is the name of their invention: the self-con- 
tained underwater breathing apparatus, better 
known as scuba. 

The most important feature of the scuba 
gear was the demand regulator, which made it 
possible for the divers to breathe air at the same 
pressure as their underwater surroundings. This 

VOLUME 2: REAL-LIFE PHYSICS 


in turn facilitated breathing in a more normal, 
comfortable manner. Another important feature 
of a modern diver’s equipment is a buoyancy 
compensation device. Like a ship atop the water, 
a diver wants to have only so much buoyancy — 
not so much that it causes him to surface. 

As for the bathyscaphe — a term whose two 
Greek roots mean “deep” and “boat” — it made its 
debut five years after scuba gear. Built by the 
Swiss physicist and adventurer Auguste Piccard 
(1884-1962), the bathyscaphe consisted of two 
compartments: a heavy steel crew cabin that was 
resistant to sea pressure, and above it, a larger, 
light container called a float. The float was filled 
with gasoline, which in this case was not used as 
fuel, but to provide extra buoyancy, because of 
the gasoline’s low specific gravity. 

When descending, the occupants of the 
bathyscaphe — there could only be two, since the 
pressurized chamber was just 79 in (2.01 m) in 
diameter — released part of the gasoline to 
decrease buoyancy. They also carried iron ballast 
pellets on board, and these they released when 
preparing to ascend. Thanks to battery-driven 
screw propellers, the bathyscaphe was much 
more maneuverable than the bathysphere had 
ever been; furthermore, it was designed to reach 
depths that Beebe and Barton could hardly have 
conceived. 

REACHING NEW DEPTHS. It 

took several years of unsuccessful dives, but in 
1953 a bathyscaphe set the first of many depth 
records. This first craft was the Trieste, manned 
by Piccard and his son Jacques, which descended 
10,335 ft (3,150 m) below the Mediterranean, off 
Capri, Italy. A year later, in the Atlantic Ocean off 
Dakar, French West Africa (now Senegal), French 
divers Georges Houot and Pierre-Henri Willm 
reached 13,287 ft (4,063 m) in the FNRS 3. 

Then in 1960, Jacques Piccard and United 
States Navy Lieutenant Don Walsh set a record 
that still stands: 35,797 ft (10,911 m) — 23% 
greater than the height of Mt. Everest, the world’s 
tallest peak. This they did in the Trieste some 250 
mi (402 km) southeast of Guam at the Mariana 
Trench, the deepest spot in the Pacific Ocean and 
indeed the deepest spot on Earth. Piccard and 
Walsh went all the way to the bottom, a descent 
that took them 4 hours, 48 minutes. Coming up 
took 3 hours, 17 minutes. 

Thirty- five years later, in 1995, the Japanese 
craft Kaiko also made the Mariana descent and 

SCIENCE DF EVERYDAY THINGS 


confirmed the measurements of Piccard and 
Walsh. But the achievement of the Kaiko was not 
nearly as impressive of that of the Trieste’s two- 
man crew: the Kaiko, in fact, had no crew. By the 
1990s, sophisticated remote-sensing technology 
had made it possible to send down unmanned 
ocean expeditions, and it became less necessary 
to expose human beings to the incredible risks 
encountered by the Piccards, Walsh, and others. 

filming titanic. An example of 
such an unmanned vessel is the one featured in 
the opening minutes of the Academy Award-win- 
ning motion picture Titanic (1997). The vessel 
itself, whose sinking in 1912 claimed more than 
1,000 lives, rests at such a great depth in the 
North Atlantic that it is impractical either to raise 
it, or to send manned expeditions to explore the 
interior of the wreck. The best solution, then, is a 
remotely operated vessel of the kind also used for 
purposes such as mapping the ocean floor, 
exploring for petroleum and other deposits, and 
gathering underwater plate technology data. 

The craft used in the film, which has “arms” 
for grasping objects, is of a variety specially 
designed for recovering items from shipwrecks. 
For the scenes that showed what was supposed to 
be the Titanic as an active vessel, director James 
Cameron used a 90% scale model that depicted 
the ship’s starboard side — the side hit by the ice- 
berg. Therefore, when showing its port side, as 
when it was leaving the Southampton, England, 
dock on April 15, 1912, all shots had to be 
reversed: the actual signs on the dock were in 
reverse lettering in order to appear correct when 
seen in the final version. But for scenes of the 
wrecked vessel lying at the bottom of the ocean, 
Cameron used the real Titanic. 

To do this, he had to use a submersible; but 
he did not want to shoot only from inside the 
submersible, as had been done in the 1992 IMAX 
film Titanica. Therefore, his brother Mike 
Cameron, in cooperation with Panavision, built a 
special camera that could withstand 400 atm 
(3.923 • 10 7 Pa) — that is, 400 times the air pres- 
sure at sea level. The camera was attached to the 
outside of the submersible, which for these exter- 
nal shots was manned by Russian submarine 
operators. 

Because the special camera only held twelve 
minutes’ worth of film, it was necessary to make 
a total of twelve dives. On the last two, a remote- 
ly operated submersible entered the wreck, which 



The divers pictured here have ascended from a 

SUNKEN SHIP AND HAVE STOPPED AT THE 1 CD-FT (3‘M) 
DECOMPRESSION LEVEL TO AVOID GETTING DECOMPRES- 
SION SICKNESS, BETTER KNOWN AS THE “BENDS.” (Pi 10 - 

tograph, copyright Jonathan Blair/Corbis. Reproduced by permission.) 


would have been too dangerous for the humans 
in the manned craft. Cameron had intended the 
remotely operated submersible as a mere prop, 
but in the end its view inside the ruined Titanic 
added one of the most poignant touches in the 
entire film. To these he later added scenes involv- 
ing objects specific to the film’s plot, such as the 
safe. These he shot in a controlled underwater 
environment designed to look like the interior of 
the Titanic. 

Into the Skies 

In the earlier description of Piccard’s bathy- 
scaphe design, it was noted that the craft consist- 
ed of two compartments: a heavy steel crew cabin 
resistant to sea pressure, and above it a larger, 
light container called a float. If this sounds rather 
like the structure of a hot-air balloon, there is no 
accident in that. 

In 1931, nearly two decades before the 
bathyscaphe made its debut, Piccard and another 
Swiss scientist, Paul Kipfer, set a record of a dif- 
ferent kind with a balloon. Instead of going lower 


science of everyday things 


VOLUME 2: REAL-LIFE PHYSICS 


BUOYANCY 


1 25 




BUDYANCY 


| 1 26 


than anyone ever had, as Piccard and his son 
Jacques did in 1953 — and as Jacques and Walsh 
did in an even greater way in 1960 — Piccard and 
Kipfer went higher than ever, ascending to 55,563 
ft (16,940 m). This made them the first two men 
to penetrate the stratosphere, which is the next 
atmospheric layer above the troposphere, a layer 
approximately 10 mi (16.1 km) high that covers 
the surface of Earth. 

Piccard, without a doubt, experienced the 
greatest terrestrial altitude range of any human 
being over a lifetime: almost 12.5 mi (20.1 km) 
from his highest high to his lowest low, 84% of it 
above sea level and the rest below. His career, 
then, was a tribute to the power of buoyant 
force — and to the power of overcoming buoyant 
force for the purpose of descending to the ocean 
depths. Indeed, the same can be said of the Pic- 
card family as a whole: not only did Jacques set 
the world’s depth record, but years later, Jacques’s 
son Bertrand took to the skies for another 
record-setting balloon flight. 

In 1999, Bertrand Piccard and British bal- 
loon instructor Brian Wilson became the first 
men to circumnavigate the globe in a balloon, the 
Breitling Orbiter 3. The craft extended 180 ft 
(54.86) from the top of the envelope — the part of 
the balloon holding buoyant gases — to the bot- 
tom of the gondola, the part holding riders. The 
pressurized cabin had one bunk in which one 
pilot could sleep while the other flew, and up 
front was a computerized control panel which 
allowed the pilot to operate the burners, switch 
propane tanks, and release empty ones. It took 
Piccard and Wilson just 20 days to circle the 
Earth — a far cry from the first days of ballooning 
two centuries earlier. 

THE FIRST BALLDDNS. The Pic- 
card family, though Swiss, are francophone; that 
is, they come from the French-speaking part of 
Switzerland. This is interesting, because the his- 
tory of human encounters with buoyancy — 
below the ocean and even more so in the air — 
has been heavily dominated by French names. In 
fact, it was the French brothers, Joseph-Michel 
(1740-1810) and Jacques-Etienne (1745-1799) 
Montgolfier, who launched the first balloon in 
1783. These two became to balloon flight what 
two other brothers, the Americans Orville and 
Wilbur Wright, became with regard to the inven- 
tion that superseded the balloon twelve decades 
later: the airplane. 

VDLUME 2: REAL-LIFE PHYSICS 


On that first flight, the Montgolfiers sent up 
a model 30 ft (9.15 m) in diameter, made of 
linen-lined paper. It reached a height of 6,000 ft 
(1,828 m), and stayed in the air for 10 minutes 
before coming back down. Eater that year, the 
Montgolfiers sent up the first balloon flight with 
living creatures — a sheep, a rooster, and a duck — 
and still later in 1783, Jean-Fran^ois Pilatre de 
Rozier (1756-1785) became the first human 
being to ascend in a balloon. 

Rozier only went up 84 ft (26 m), which was 
the length of the rope that tethered him to the 
ground. As the makers and users of balloons 
learned how to use ballast properly, however, 
flight times were extended, and balloon flight 
became ever more practical. In fact, the world’s 
first military use of flight dates not to the twenti- 
eth century but to the eighteenth — 1794, specifi- 
cally, when France created a balloon corps. 

H □ W A BALLDON FLOATS. 

There are only three gases practical for lifting a 
balloon: hydrogen, helium, and hot air. Each is 
much less than dense than ordinary air, and this 
gives them their buoyancy. In fact, hydrogen is 
the lightest gas known, and because it is cheap to 
produce, it would be ideal — except for the fact 
that it is extremely flammable. After the 1937 
crash of the airship Hindenburg, the era of 
hydrogen use for lighter-than-air transport effec- 
tively ended. 

Helium, on the other hand, is perfectly safe 
and only slightly less buoyant than hydrogen. 
This makes it ideal for balloons of the sort that 
children enjoy at parties; but helium is expensive, 
and therefore impractical for large balloons. 
Hence, hot air — specifically, air heated to a tem- 
perature of about 570°F (299°C), is the only truly 
viable option. 

Charles’s law, one of the laws regarding the 
behavior of gases, states that heating a gas will 
increase its volume. Gas molecules, unlike their 
liquid or solid counterparts, are highly non- 
attractive — that is, they tend to spread toward 
relatively great distances from one another. There 
is already a great deal of empty space between gas 
molecules, and the increase in volume only 
increases the amount of empty space. Hence, 
density is lowered, and the balloon floats. 

airships. Around the same time the 
Montgolfier brothers launched their first bal- 
loons, another French designer, Jean-Baptiste- 
Marie Meusnier, began experimenting with a 

SCIENCE OF EVERYDAY THINGS 


Buoyancy 



□ nce considered obsolete, blimps are enjoying a renaissance among scientists and government agen- 
cies. The blimp pictured here, the Aerostat blimp, is equipped with radar for drug enforcement and 
instruments for weather observation. (Corbis. Reproduced by permission.) 


more streamlined, maneuverable model. Early 
balloons, after all, could only be maneuvered 
along one axis, up and down: when it came to 
moving sideways or forward and backward, they 
were largely at the mercy of the elements. 

It was more than a century before 
Meusnier’s idea — the prototype for an airship — 
became a reality. In 1898, Alberto Santos- 
Dumont of Brazil combined a balloon with a 
propeller powered by an internal-combustion 
instrument, creating a machine that improved on 
the balloon, much as the bathyscaphe later 
improved on the bathysphere. Santos-Dumont’s 
airship was non-rigid, like a balloon. It also used 
hydrogen, which is apt to contract during descent 
and collapse the envelope. To counter this prob- 
lem, Santos-Dumont created the ballonet, an 
internal airbag designed to provide buoyancy 
and stabilize flight. 

One of the greatest figures in the history of 
lighter-than-air flight — a man whose name, 
along with blimp and dirigible, became a syn- 
onym for the airship — was Count Ferdinand von 
Zeppelin (1838-1917). It was he who created a 
lightweight structure of aluminum girders and 
rings that made it possible for an airship to 
remain rigid under varying atmospheric condi- 

SCIENCE □ E EVERYDAY THINGS 


tions. Yet Zeppelin’s earliest launches, in the 
decade that followed 1898, were fraught with a 
number of problems — not least of which were 
disasters caused by the flammability of hydrogen. 

Zeppelin was finally successful in launching 
airships for public transport in 1911, and the 
quarter-century that followed marked the golden 
age of airship travel. Not that all was “golden” 
about this age: in World War I, Germany used 
airships as bombers, launching the first London 
blitz in May 1915. By the time Nazi Germany ini- 
tiated the more famous World War II London 
blitz 25 years later, ground-based anti-aircraft 
technology would have made quick work of any 
zeppelin; but by then, airplanes had long since 
replaced airships. 

During the 1920s, though, airships such as 
the Graf Zeppelin competed with airplanes as a 
mode of civilian transport. It is a hallmark of the 
perceived safety of airships over airplanes at the 
time that in 1928, the Graf Zeppelin made its first 
transatlantic flight carrying a load of passengers. 
Just a year earlier, Charles Lindbergh had made 
the first-ever solo, nonstop transatlantic flight in 
an airplane. Today this would be the equivalent 
of someone flying to the Moon, or perhaps even 
Mars, and there was no question of carrying pas- 

VDLUME 2: REAL-LIFE PHYSICS 


1 27 


BUDYANCY 


KEY TERMS 


ARCHIMEDES’S PRINCIPLE: A rule 

of physics which holds that the buoyant 
force of an object immersed in fluid is 
equal to the weight of the fluid displaced 
by the object. It is named after the Greek 
mathematician, physicist, and inventor 
Archimedes (c. 287-212 b.c.), who first 
identified it. 

ballast: A heavy substance that, by 

increasing the weight of an object experi- 
encing buoyancy, improves its stability. 

budyancy: The tendency of an object 

immersed in a fluid to float. This can be 
explained by Archimedes’s principle. 

d e n s i ty: Mass divided by volume. 

displacement: A measure of the 

weight of the fluid that has had to be 
moved out of position so that an object can 
be immersed. If a ship set down in the 
ocean causes 1,000 tons of water to be dis- 
placed, it is said to possess a displacement 
of 1,000 tons. 

fluid: Any substance, whether gas or 

liquid, that conforms to the shape of its 
container. 

force: The product of mass multi- 

plied by acceleration. 


mass: A measure of inertia, indicating 

the resistance of an object to a change in its 
motion. For an object immerse in fluid, 
mass is equal to volume multiplied by 
density. 

pressure: The exertion of force 

over a two-dimensional area; hence the 
formula for pressure is force divided by 
area. The British system of measures typi- 
cally reckons pressure in pounds per 
square inch. In metric terms, this is meas- 
ured in terms of newtons (N) per square 
meter, a figure known as a pascal (Pa.) 

specific gravity: The density of 

an object or substance relative to the densi- 
ty of water; or more generally, the ratio 
between the densities of two objects or 
substances. 

volume: The amount of three- 

dimensional space occupied by an object. 
Volume is usually measured in cubic units. 

weight: A force equal to mass multi- 

plied by the acceleration due to gravity (32 
ft/9.8 m/sec 2 ). For an object immersed in 
fluid, weight is the same as volume multi- 
plied by density multiplied by gravitation- 
al acceleration. 


| 1 ZB 


sengers. Furthermore, Lindbergh was celebrated 
as a hero for the rest of his life, whereas the pas- 
sengers aboard the Graf Zeppelin earned no more 
distinction for bravery than would pleasure- 
seekers aboard a cruise. 

THE LIMITATIONS OF LIGHT- 

er-than-air transport. For a 

few years, airships constituted the luxury liners of 
the skies; but the Hindenburg crash signaled the 
end of relatively widespread airship transport. In 
any case, by the time of the 1937 Hindenburg 
crash, lighter-than-air transport was no longer 

VOLUME 2: REAL-LIFE PHYSICS 


the leading contender in the realm of flight tech- 
nology. 

Ironically enough, by 1937 the airplane had 
long since proved itself more viable — even 
though it was actually heavier than air. The prin- 
ciples that make an airplane fly have little to do 
with buoyancy as such, and involve differences in 
pressure rather than differences in density. Yet 
the replacement of lighter-than-air craft on the 
cutting edge of flight did not mean that balloons 
and airships were relegated to the museum; 
instead, their purposes changed. 

SCIENCE DF EVERYDAY THINGS 



Buoyancy 


The airship enjoyed a brief resurgence of 
interest during World War II, though purely as a 
surveillance craft for the United States military. 
In the period after the war, the U.S. Navy hired 
the Goodyear Tire and Rubber Company to pro- 
duce airships, and as a result of this relationship 
Goodyear created the most visible airship since 
the Graf Zeppelin and the Hindenburg: the 
Goodyear Blimp. 

BLIMPS AND BALLOONS: ON 

THE DU TT I N G EDGE?. The blimp, 
known to viewers of countless sporting events, is 
much better-suited than a plane or helicopter to 
providing TV cameras with an aerial view of a 
stadium — and advertisers with a prominent bill- 
board. Military forces and science communities 
have also found airships useful for unexpected 
purposes. Their virtual invisibility with regard to 
radar has reinvigorated interest in blimps on the 
part of the U.S. Department of Defense, which 
has discussed plans to use airships as radar plat- 
forms in a larger Strategic Air Initiative. In addi- 
tion, French scientists have used airships for 
studying rain forest treetops or canopies. 

Balloons have played a role in aiding space 
exploration, which is emblematic of the relation- 
ship between lighter-than-air transport and 
more advanced means of flight. In 1961, Mal- 
colm D. Ross and Victor A. Prother of the U.S. 
Navy set the balloon altitude record with a height 
of 113,740 ft (34,668 m.) The technology that 
enabled their survival at more than 21 mi (33.8 
km) in the air was later used in creating life-sup- 
port systems for astronauts. 

Balloon astronomy provides some of the 
clearest images of the cosmos: telescopes mount- 
ed on huge, unmanned balloons at elevations as 
high as 120,000 ft (35,000 m) — far above the dust 


and smoke of Earth — offer high-resolution 
images. Balloons have even been used on other 
planets: for 46 hours in 1985, two balloons 
launched by the unmanned Soviet expedition to 
Venus collected data from the atmosphere of that 
planet. 

American scientists have also considered a 
combination of a large hot-air balloon and a 
smaller helium-filled balloon for gathering data 
on the surface and atmosphere of Mars during 
expeditions to that planet. As the air balloon is 
heated by the Sun’s warmth during the day, it 
would ascend to collect information on the 
atmosphere. (In fact the “air” heated would be 
from the atmosphere of Mars, which is com- 
posed primarily of carbon dioxide.) Then at 
night when Mars cools, the air balloon would 
lose its buoyancy and descend, but the helium 
balloon would keep it upright while it collected 
data from the ground. 

WHERE T □ LEARN MORE 

“Buoyancy” (Web site), <http://www.aquaholic.com/ 
gasses/laws.htm> (March 12, 2001). 

“Buoyancy” (Web site), <http://www.uncwil.edu/nurc/ 
aquarius/lessons/buoyancy.htm> (March 12, 2001). 

“Buoyancy Basics” Nova/PBS (Web site). 

<http://www.pbs.org/wgbh/nova/lasalle/buoybasics. 
html> (March 12, 2001). 

Challoner, Jack. Floating and Sinking. Austin, TX: Rain- 
tree Steck- Vaughn, 1997. 

Cobb, Allan B. Super Science Projects About Oceans. New 
York: Rosen, 2000. 

Gibson, Gary. Making Things Float and Sink. Illustrated 
by Tony Kenyon. Brookfield, CT: Copper Beeck 
Brooks, 1995. 

Taylor, Barbara. Liquid and Buoyancy. New York: War- 
wick Press, 1990. 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 29 





S TAT ICS AND 
EQUILIBRIUM 


C □ N C E PT 

Statics, as its name suggests, is the study of bod- 
ies at rest. Those bodies may be acted upon by a 
variety of forces, but as long as the lines of force 
meet at a common point and their vector sum is 
equal to zero, the body itself is said to be in a state 
of equilibrium. Among the topics of significance 
in the realm of statics is center of gravity, which 
is relatively easy to calculate for simple bodies, 
but much more of a challenge where aircraft or 
ships are concerned. Statics is also applied in 
analysis of stress on materials — from a picture 
frame to a skyscraper. 

H □ W IT WDRKS 

Equilibrium and Vectors 

Essential to calculations in statics is the use of 
vectors, or quantities that have both magnitude 
and direction. By contrast, a scalar has only mag- 
nitude. If one says that a certain piece of proper- 
ty has an area of one acre, there is no directional 
component. Nor is there a directional compo- 
nent involved in the act of moving the distance of 
1 mi (1.6 km), since no statement has been made 
as to the direction of that mile. On the other 
hand, if someone or something experiences a dis- 
placement, or change in position, of 1 mi to the 
northeast, then what was a scalar description has 
been placed in the language of vectors. 

Not only are mass and speed (as opposed to 
velocity) considered scalars; so too is time. This 
might seem odd at first glance, but — on Earth at 
least, and outside any special circumstances 
posed by quantum mechanics — time can only 
move forward. Hence, direction is not a factor. By 

SCIENCE □ F EVERYDAY THINGS 


contrast, force, equal to mass multiplied by 
acceleration, is a vector. So too is weight, a spe- 
cific type of force equal to mass multiplied by 
the acceleration due to gravity (32 ft or [9.8 m] / 
sec 2 ). Force may be in any direction, but the 
direction of weight is always downward along a 
vertical plane. 

vector sums. Adding scalars is 
simple, since it involves mere arithmetic. The 
addition of vectors is more challenging, and usu- 
ally requires drawing a diagram, for instance, if 
trying to obtain a vector sum for the velocity of a 
car that has maintained a uniform speed, but has 
changed direction several times. 

One would begin by representing each vec- 
tor as an arrow on a graph, with the tail of each 
vector at the head of the previous one. It would 
then be possible to draw a vector from the tail of 
the first to the head of the last. This is the sum of 
the vectors, known as a resultant, which meas- 
ures the net change. 

Suppose, for instance, that a car travels 
north 5 mi (8 km), east 2 mi (3.2 km), north 3 mi 
(4.8 km), east 3 mi, and finally south 3 mi. One 
must calculate its net displacement — in other 
words, not the sum of all the miles it has traveled, 
but the distance and direction between its start- 
ing point and its end point. First, one draws the 
vectors on a piece of graph paper, using a logical 
system that treats the y axis as the north-south 
plane, and the x axis as the east-west plane. Each 
vector should be in the form of an arrow point- 
ing in the appropriate direction. 

Having drawn all the vectors, the only 
remaining one is between the point where the 
car’s journey ends and the starting point — that 
is, the resultant. The number of sides to the 

VDLUME Z: REAL-LIFE PHYSICS 


1 33 



Statics and 
Equilibrium 


resulting shape is always one more than the num- 
ber of vectors being added; the final side is the 
resultant. 

In this particular case, the answer is fairly 
easy. Because the car traveled north 5 mi and ulti- 
mately moved east by 5 mi, returning to a posi- 
tion of 5 mi north, the segment from the result- 
ant forms the hypotenuse of an equilateral (that 
is, all sides equal) right triangle. By applying the 
Pythagorean theorem, which states that the 
square of the length of the hypotenuse is equal to 
the sum of the squares of the other two sides, one 
quickly arrives at a figure of 7.07 m (11.4 km) in 
a northeasterly direction. This is the car’s net dis- 
placement. 

Calculating Force and Ten- 
sion in Equilibrium 

Using vector sums, it is possible to make a num- 
ber of calculations for objects in equilibrium, but 
these calculations are somewhat more challeng- 
ing than those in the car illustration. One form of 
equilibrium calculation involves finding tension, 
or the force exerted by a supporting object on an 
object in equilibrium — a force that is always 
equal to the amount of weight supported. 
(Another way of saying this is that if the tension 
on the supporting object is equal to the weight it 
supports, then the supported object is in equilib- 
rium.) 

In calculations for tension, it is best to treat 
the supporting object — whether it be a rope, pic- 
ture hook, horizontal strut or some other item — 
as though it were weightless. One should begin 
by drawing a free-body diagram, a sketch show- 
ing all the forces acting on the supported object. 
It is not necessary to show any forces (other than 
weight) that the object itself exerts, since those 
do not contribute to its equilibrium. 

RESDLVING X AND Y COMPO- 
NENT s . As with the distance vector graph 
discussed above, next one must equate these 
forces to the x and y axes. The distance graph 
example involved only segments already parallel 
to x and y, but suppose — using the numbers 
already discussed — the graph had called for the 
car to move in a perfect 45°-angle to the north- 
east along a distance of 7.07 mi. It would then 
have been easy to resolve this distance into an x 
component (5 mi east) and a y component (5 mi 
north) — which are equal to the other two sides of 
the equilateral triangle. 


This resolution of x and y components is 
more challenging for calculations involving equi- 
librium, but once one understands the principle 
involved, it is easy to apply. For example, imagine 
a box suspended by two ropes, neither of which 
is at a 90°-angle to the box. Instead, each rope is 
at an acute angle, rather like two segments of a 
chain holding up a sign. 

The x component will always be the product 
of tension (that is, weight) multiplied by the 
cosine of the angle. In a right triangle, one angle 
is always equal to 90°, and thus by definition, the 
other two angles are acute, or less than 90°. The 
angle of either rope is acute, and in fact, the rope 
itself may be considered the hypotenuse of an 
imaginary triangle. The base of the triangle is the 
x axis, and the angle between the base and the 
hypotenuse is the one under consideration. 

Hence, we have the use of the cosine, which 
is the ratio between the adjacent leg (the base) of 
the triangle and the hypotenuse. Regardless of 
the size of the triangle, this figure is a constant for 
any particular angle. Likewise, to calculate the y 
component of the angle, one uses the sine, or the 
ratio between the opposite side and the 
hypotenuse. Keep in mind, once again, that the 
adjacent leg for the angle is by definition the 
same as the x axis, just as the opposite leg is the 
same as the y axis. The cosine (abbreviated cos), 
then, gives the x component of the angle, as the 
sine (abbreviated sin) does the y component. 

REAL-LIFE 
A P P L I C AT IONS 

Equilibrium and Center of 
Gravity in Real Objects 

Before applying the concept of vector sums to 
matters involving equilibrium, it is first necessary 
to clarify the nature of equilibrium itself — what 
it is and what it is not. Earlier it was stated that an 
object is in equilibrium if the vector sum of the 
forces acting on it are equal to zero — as long as 
those forces meet at a common point. 

This is an important stipulation, because it is 
possible to have lines of force that cancel one 
another out, but nonetheless cause an object to 
move. If a force of a certain magnitude is applied 
to the right side of an object, and a line of force 
of equal magnitude meets it exactly from the left, 
then the object is in equilibrium. But if the line of 


| 1 34 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 


Statics and 
Equilibrium 


force from the right is applied to the top of the 
object, and the line of force from the left to the 
bottom, then they do not meet at a common 
point, and the object is not in equilibrium. 
Instead, it is experiencing torque, which will 
cause it to rotate. 

VARIETIES OF EQUILIBRIUM. 

There are two basic conditions of equilibrium. 
The term “translational equilibrium” describes 
an object that experiences no linear (straight- 
line) acceleration; on the other hand, an object 
experiencing no rotational acceleration (a com- 
ponent of torque) is said to be in rotational equi- 
librium. 

Typically, an object at rest in a stable situa- 
tion experiences both linear and rotational equi- 
librium. But equilibrium itself is not necessarily 
stable. An empty glass sitting on a table is in sta- 
ble equilibrium: if it were tipped over slightly — 
that is, with a force below a certain threshold — 
then it would return to its original position. This 
is true of a glass sitting either upright or upside- 
down. 

Now imagine if the glass were somehow 
propped along the edge of a book sitting on the 
table, so that the bottom of the glass formed the 
hypotenuse of a triangle with the table as its base 
and the edge of the book as its other side. The 
glass is in equilibrium now, but unstable equilib- 
rium, meaning that a slight disturbance — a force 
from which it could recover in a stable situa- 
tion — would cause it to tip over. 

If, on the other hand, the glass were lying on 
its side, then it would be in a state of neutral 
equilibrium. In this situation, the application of 
force alongside the glass will not disturb its equi- 
librium. The glass will not attempt to seek stable 
equilibrium, nor will it become more unstable; 
rather, all other things being equal, it will remain 
neutral. 

center df gravity. Center of 
gravity is the point in an object at which the 
weight below is equal to the weight above, the 
weight in front equal to the weight behind, and 
the weight to the left equal to the weight on the 
right. Every object has just one center of gravity, 
and if the object is suspended from that point, it 
will not rotate. 

One interesting aspect of an object’s center 
of gravity is that it does not necessarily have to be 
within the object itself. When a swimmer is 
poised in a diving stance, as just before the start - 

SCIENCE OF EVERYDAY THINGS 



A GLASS SITTING GN A TABLE IS IN A STATE DF STABLE 

equilibrium. (Photograph by John Wilkes Studio/Corbis. Repro- 
duced by permission.) 

ing bell in an Olympic competition, the swim- 
mer’s center of gravity is to the front — some dis- 
tance from his or her chest. This is appropriate, 
since the objective is to get into the water as 
quickly as possible once the race starts. 

By contrast, a sprinter’s stance places the 
center of gravity well within the body, or at least 
firmly surrounded by the body — specifically, at 
the place where the sprinter’s rib cage touches the 
forward knee. This, too, fits with the needs of the 
athlete in the split-second following the starting 
gun. The sprinter needs to have as much traction 
as possible to shoot forward, rather than forward 
and downward, as the swimmer does. 

Tension Calculations 

In the earlier discussion regarding the method of 
calculating tension in equilibrium, two of the 
three steps of this process were given: first, draw 
a free-body diagram, and second, resolve the 
forces into x and y components. The third step is 
to set the force components along each axis equal 
to zero — since, if the object is truly in equilibri- 
um, the sum of forces will indeed equal zero. This 
makes it possible, finally, to solve the equations 
for the net tension. 

VDLUME 2: REAL-LIFE PHYSIGS 


1 35 



In the starting blocks, a sprinter’s center of gravity is aligned along the rib cage and forward knee, 
thus maximizing the runner’s ability to shoot FORWARD out of the blocks. (Photograph by Ronnen Eshel/Corbis. 
Reproduced by permission.) 


| 1 36 


Imagine a picture that weighs 100 lb (445 N) 
suspended by a wire, the left side of which may be 
called segment A, and the right side segment B. 
The wire itself is not perfectly centered on the 
picture-hook: A is at a 30° angle, and Bona 45° 
angle. It is now possible to find the tension on 
both. 

First, one can resolve the horizontal compo- 
nents by the formula F x = T Bx + T M - 0, meaning 
that the x component of force is equal to the 
product of tension for the x component of B, 
added to the product of tension for the x compo- 
nent of A, which in turn is equal to zero. Given 
the 30°-angle of A, ^ — 0.866, which is the cosine 
of 30%, is equal to cos 45°, which equals 0.707. 
(Recall the earlier discussion of distance, in 
which a square with sides 5 mi long was 
described: its hypotenuse was 7.07 mi, and 5/7.07 
= 0.707.) 

Because A goes off to the left from the point 
at which the picture is attached to the wire, this 
places it on the negative portion of the x axis. 
Therefore, the formula can now be restated as 
r B (0.707)-T A (0.866) = 0. Solving for T B reveals 
that it is equal to T A { 0.866/0.707) = (1.22)T A . 
This will be substituted for T B in the formula for 
the total force along the y component. 

VDLUME 2: REAL-LIFE PHYSICS 


However, the y-force formula is somewhat 
different than for x: since weight is exerted along 
the y axis, it must be subtracted. Thus, the for- 
mula for the y component of force is F = T Ay + 
T By -w = 0. (Note that the y components of both 
A and B are positive: by definition, this must be 
so for an object suspended from some height.) 

Substituting the value for T B obtained above, 

(1.22) T a , makes it possible to complete the equa- 

tion. Since the sine of 30° is 0.5, and the sine of 
45° is 0.707 — the same value as its cosine — one 
can state the equation thus: T A ( 0.5) + 

(1.22) T a ( 0.707)-100 lb = 0. This can be restated 
as T A ( 0.5 + (1.22 • 0.707)) = T A (1.36) = 100 lb. 
Hence, T A = (100 lb/1.36) = 73.53 lb. Since T B = 

(1.22 ) T a , this yields a value of 89.71 lb for T B . 

Note that T A and T B actually add up to con- 
siderably more than 100 lb. This, however, is 
known as an algebraic sum — which is very simi- 
lar to an arithmetic sum, inasmuch as algebra is 
simply a generalization of arithmetic. What is 
important here, however, is the vector sum, and 
the vector sum of T A and T B equals 100 lb. 

CALCULATING CENTER OF 

gravity. Rather than go through another 
lengthy calculation for center of gravity, we will 
explain the principles behind such calculations. 

SCIENCE OF EVERYDAY THINGS 



It is easy to calculate the center of gravity for a 
regular shape, such as a cube or sphere — assum- 
ing, of course, that the mass and therefore the 
weight is evenly distributed throughout the 
object. In such a case, the center of gravity is the 
geometric center. For an irregular object, howev- 
er, center of gravity must be calculated. 

An analogy regarding United States demo- 
graphics may help to highlight the difference 
between geometric center and center of gravity. 
The geographic center of the U.S., which is anal- 
ogous to geometric center, is located near the 
town of Castle Rock in Butte County, South 
Dakota. (Because Alaska and Hawaii are so far 
west of the other 48 states — and Alaska, with its 
great geographic area, is far to the north — the 
data is skewed in a northwestward direction. The 
geographic center of the 48 contiguous states is 
near Lebanon, in Smith County, Kansas.) 

The geographic center, like the geometric 
center of an object, constitutes a sort of balance 
point in terms of physical area: there is as much 
U.S. land to the north of Castle Rock, South 
Dakota, as to the south, and as much to the east 
as to the west. The population center is more like 
the center of gravity, because it is a measure, in 
some sense, of “weight” rather than of volume — 
though in this case concentration of people is 
substituted for concentration of weight. Put 
another way, the population center is the balance 
point of the population, if it were assumed that 
every person weighed the same amount. 

Naturally, the population center has been 
shifting westward ever since the first U.S. census 
in 1790, but it is still skewed toward the east: 
though there is far more U.S. land west of the 
Mississippi River, there are still more people east 
of it. Hence, according to the 1990 U.S. census, 
the geographic center is some 1,040 mi (1,664 
km) in a southeastward direction from the pop- 
ulation center: just northwest of Steelville, Mis- 
souri, and a few miles west of the Mississippi. 

The United States, obviously, is an “irregular 
object,” and calculations for either its geographic 
or its population center represent the mastery of 
numerous mathematical principles. How, then, 
does one find the center of gravity for a much 
smaller irregular object? There are a number of 
methods, all rather complex. 

To measure center of gravity in purely phys- 
ical terms, there are a variety of techniques relat- 


ing to the shape of the object to be measured. 
There is also a mathematical formula, which 
involves first treating the object as a conglomera- 
tion of several more easily measured objects. 
Then the x components for the mass of each 
“sub-object” can be added, and divided by the 
combined mass of the object as a whole. The 
same can be done for the y components. 

Using Equilibrium Calcula- 
tions 

One reason for making center of gravity calcula- 
tions is to ensure that the net force on an object 
passes through that center. If it does not, the 
object will start to rotate — and for an airplane, 
for instance, this could be disastrous. Hence, the 
builders and operators of aircraft make exceed- 
ingly detailed, complicated calculations regard- 
ing center of gravity. The same is true for ship- 
builders and shipping lines: if a ship’s center of 
gravity is not vertically aligned with the focal 
point of the buoyant force exerted on it by the 
water, it may well sink. 

In the case of ships and airplanes, the shapes 
are so irregular that center of gravity calculations 
require intensive analyses of the many compo- 
nents. Hence, a number of companies that supply 
measurement equipment to the aerospace and 
maritime industries offer center of gravity meas- 
urement instruments that enable engineers to 
make the necessary calculations. 

On dry ground, calculations regarding equi- 
librium are likewise quite literally a life and death 
matter. In the earlier illustration, the object in 
equilibrium was merely a picture hanging from a 
wire — but what if it were a bridge or a building? 
The results of inaccurate estimates of net force 
could affect the lives of many people. Hence, 
structural engineers make detailed analyses of 
stress, once again using series of calculations that 
make the picture-frame illustration above look 
like the simplest of all arithmetic problems. 

WHERE T □ LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Determining Center of Gravity” National Aeronautics 
and Space Administration (Web site). 
<http://www.grc.nasa.gov/WWW/K-12/airplane/cg. 
html> (March 19, 2001). 


Statics and 
Equilibrium 


SCIENCE □ F EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 


1 37 


Statics and 
Equilibrium 


KEY TERMS 


acceleration: A change in velocity. 

center of GRAVITY: The point on 

an object at which the total weights on 
either side of all axes (x, y, and z) are iden- 
tical. Each object has just one center of 
gravity, and if it is suspended from that 
point, it will be in a state of perfect rota- 
tional equilibrium. 

cosine: For an acute (less than 90°) 

angle in a right triangle, the cosine (abbre- 
viated cos) is the ratio between the adja- 
cent leg and the hypotenuse. Regardless of 
the size of the triangle, this figure is a con- 
stant for any particular angle. 

displacement: Change in position. 

equilibrium: A state in which vector 

sum for all lines of force on an object is 
equal to zero. An object that experiences no 
linear acceleration is said to be in transla- 
tional equilibrium, and one that experi- 
ences no rotational acceleration is referred 
to as being in rotational equilibrium. An 
object may also be in stable, unstable, or 
neutral equilibrium. 

force: The product of mass multi- 

plied by acceleration. 

FREE-BODY DIAGRAM: A sketch 

showing all the outside forces acting on an 
object in equilibrium. 

hypotenuse: In a right triangle, the 

side opposite the right angle. 

resultant: The sum of two or more 

vectors, which measures the net change in 
distance and direction. 

right triangle: A triangle that 

includes a right (90°) angle. The other 
two angles are, by definition, acute, or less 
than 90°. 


scalar: A quantity that possesses 

only magnitude, with no specific direction. 
Mass, time, and speed are all scalars. The 
opposite of a scalar is a vector. 

sine: For an acute (less than 90°) angle 

in a right triangle, the sine (abbreviated 
sin) is the ratio between the opposite leg 
and the hypotenuse. Regardless of the size 
of the triangle, this figure is a constant for 
any particular angle. 

statics: The study of bodies at rest. 

Those bodies may be acted upon by a vari- 
ety of forces, but as long as the vector sum 
for all those lines of force is equal to zero, 
the body itself is said to be in a state of 
equilibrium. 

tension: The force exerted by a sup- 

porting object on an object in equilibri- 
um — a force that is always equal to the 
amount of weight supported. 

vector: A quantity that possesses 

both magnitude and direction. Force is a 
vector; so too is acceleration, a component 
of force; and likewise weight, a variety of 
force. The opposite of a vector is a scalar. 

vectdr sum: A calculation, made by 

different methods according to the factor 
being analyzed — for instance, velocity or 
force — that yields the net result of all the 
vectors applied in a particular situation. 

ve ld c ity: The speed of an object in a 

particular direction. Velocity is thus a vec- 
tor quantity. 

weight: A measure of the gravitation- 

al force on an object; the product of mass 
multiplied by the acceleration due to 
gravity. 


| 1 38 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 



“Equilibrium and Statics” (Web site). <http://www. 
glenbrook.kl2.il.us/gbssci/phys/Class/vectors/u313c. 
html> (March 19, 2001). 

“Exploratorium Snack: Center of Gravity.” The Explorato- 
rium (Web site), <http://www.exploratorium.edu/ 
snacks/center_of_gravity.html> (March 19, 2001). 

Faivre d’Arcier, Marima. What Is Balance? Illustrated by 
Volker Theinhardt. New York: Viking Kestrel, 1986. 

Taylor, Barbara. Weight and Balance. Photographs by 
Peter Millard. New York: F. Watts, 1990. 


“Where Is Your Center of Gravity?" The K-8 Aeronautics 
Internet Textbook (Web site). <http://wing.ucdavis. 
edu/Curriculums/Forces_Motion/center_howto. 
html> (March 19, 2001). 

Wood, Robert W. Mechanics Fundamentals. Illustrated by 
Bill Wright. Philadelphia, PA: Chelsea House, 1997. 

Zubrowski, Bernie. Mobiles: Building and Experimenting 
with Balancing Toys. Illustrated by Roy Doty. New 
York: Morrow Junior Books, 1993. 


Statics and 
Equilibrium 


1 39 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


PRESSURE 


C □ N C E PT 

Pressure is the ratio of force to the surface area 
over which it is exerted. Though solids exert pres- 
sure, the most interesting examples of pressure 
involve fluids — that is, gases and liquids — and in 
particular water and air. Pressure plays a number 
of important roles in daily life, among them its 
function in the operation of pumps and 
hydraulic presses. The maintenance of ordinary 
air pressure is essential to human health and 
well-being: the body is perfectly suited to the 
ordinary pressure of the atmosphere, and if that 
pressure is altered significantly, a person may 
experience harmful or even fatal side-effects. 

H □ W IT WDRKS 

Force and Surface Area 

When a force is applied perpendicular to a sur- 
face area, it exerts pressure on that surface equal 
to the ratio of F to A, where F is the force and A 
the surface area. Hence, the formula for pressure 
(p) is p = FI A. One interesting consequence of 
this ratio is the fact that pressure can increase or 
decrease without any change in force — in other 
words, if the surface becomes smaller, the pres- 
sure becomes larger, and vice versa. 

If one cheerleader were holding another 
cheerleader on her shoulders, with the girl above 
standing on the shoulder blades of the girl below, 
the upper girl’s feet would exert a certain pres- 
sure on the shoulders of the lower girl. This pres- 
sure would be equal to the upper girl’s weight (F, 
which in this case is her mass multiplied by the 
downward acceleration due to gravity) divided 
by the surface area of her feet. Suppose, then, that 

VDLUME 2: REAL-LIFE PHYSICS 


the upper girl executes a challenging acrobatic 
move, bringing her left foot up to rest against her 
right knee, so that her right foot alone exerts the 
full force of her weight. Now the surface area on 
which the force is exerted has been reduced to 
half its magnitude, and thus the pressure on the 
lower girl’s shoulder is twice as great. 

For the same reason — that is, that reduction 
of surface area increases net pressure — a well- 
delivered karate chop is much more effective 
than an open-handed slap. If one were to slap a 
board squarely with one’s palm, the only likely 
result would be a severe stinging pain on the 
hand. But if instead one delivered a blow to the 
board, with the hand held perpendicular — pro- 
vided, of course, one were an expert in karate — 
the board could be split in two. In the first 
instance, the area of force exertion is large and 
the net pressure to the board relatively small, 
whereas in the case of the karate chop, the surface 
area is much smaller — and hence, the pressure is 
much larger. 

Sometimes, a greater surface area is prefer- 
able. Thus, snowshoes are much more effective 
for walking in snow than ordinary shoes or 
boots. Ordinary footwear is not much larger than 
the surface of one’s foot, perfectly appropriate for 
walking on pavement or grass. But with deep 
snow, this relatively small surface area increases 
the pressure on the snow, and causes one’s feet to 
sink. The snowshoe, because it has a surface area 
significantly larger than that of a regular shoe, 
reduces the ratio of force to surface area and 
therefore, lowers the net pressure. 

The same principle applies with snow skis 
and water skis. Like a snowshoe, a ski makes it 
possible for the skier to stay on the surface of the 

SCIENCE □ F EVERYDAY THINGS 



snow, but unlike a snowshoe, a ski is long and 
thin, thus enabling the skier to glide more effec- 
tively down a snow-covered hill. As for skiing on 
water, people who are experienced at this sport 
can ski barefoot, but it is tricky. Most beginners 
require water skis, which once again reduce the 
net pressure exerted by the skier’s weight on the 
surface of the water. 

Measuring Pressure 

Pressure is measured by a number of units in the 
English and metric — or, as it is called in the sci- 
entific community, SI — systems. Because p = 
FI A, all units of pressure represent some ratio of 
force to surface area. The principle SI unit is 
called a pascal (Pa), or 1 N/m 2 . A newton (N), 
the SI unit of force, is equal to the force required 
to accelerate 1 kilogram of mass at a rate of 1 
meter per second squared. Thus, a Pascal is equal 
to the pressure of 1 newton over a surface area of 
1 square meter. 

In the English or British system, pressure is 
measured in terms of pounds per square inch, 
abbreviated as lbs./in 2 . This is equal to 6.89 • 10 3 
Pa, or 6,890 Pa. Scientists — even those in the 
United States, where the British system of units 
prevails — prefer to use SI units. However, the 
British unit of pressure is a familiar part of an 
American driver’s daily life, because tire pressure 
in the United States is usually reckoned in terms 
of pounds per square inch. (The recommended 
tire pressure for a mid-sized car is typically 
30-35 lb/in 2 .) 

Another important measure of pressure is 
the atmosphere (atm), which the average pres- 
sure exerted by air at sea level. In English units, 
this is equal to 14.7 lbs./in 2 , and in SI units to 
1.013 • 10 5 Pa — that is, 101,300 Pa. There are also 
two other specialized units of pressure measure- 
ment in the SI system: the bar, equal to 10 5 Pa, 
and the torr, equal to 133 Pa. Meteorologists, sci- 
entists who study weather patterns, use the mil- 
libar (mb), which, as its name implies, is equal to 
0.001 bars. At sea level, atmospheric pressure is 
approximately 1,013 mb. 

the bardmeter. The torr, once 
known as the “millimeter of mercury,” is equal to 
the pressure required to raise a column of mer- 
cury (chemical symbol Hg) 1 mm. It is named 
for the Italian physicist Evangelista Torricelli 
(1608-1647), who invented the barometer, an 
instrument for measuring atmospheric pressure. 

SCIENCE □ F EVERYDAY THINGS 



In the instance of one cheerleader standing dn 
another’s shoulders, the cheerleader’s feet 

EXERT DOWNWARD PRESSURE ON HER PARTNER’S 
SHOULDERS. THE PRESSURE IS EQUAL TO THE GIRL’S 
WEIGHT DIVIDED BY THE SURFACE AREA OF HER FEET. 

(Photograph by James L. Amos/Corbis. Reproduced by permission.) 

The barometer, constructed by Torricelli in 
1643, consisted of a long glass tube filled with 
mercury. The tube was open at one end, and 
turned upside down into a dish containing more 
mercury: hence, the open end was submerged in 
mercury while the closed end at the top consti- 
tuted a vacuum — that is, an area in which the 
pressure is much lower than 1 atm. 

The pressure of the surrounding air pushed 
down on the surface of the mercury in the bowl, 
while the vacuum at the top of the tube provided 
an area of virtually no pressure, into which the 
mercury could rise. Thus, the height to which the 
mercury rose in the glass tube represented nor- 
mal air pressure (that is, 1 atm.) Torricelli dis- 
covered that at standard atmospheric pressure, 
the column of mercury rose to 760 millimeters. 

The value of 1 atm was thus established as 
equal to the pressure exerted on a column of 
mercury 760 mm high at a temperature of 0°C 
(32°F). Furthermore, Torricelli’s invention even- 
tually became a fixture both of scientific labora- 

VDLUME 2: REAL-LIFE PHYSIGS 


PRESSURE 


1 4 1 


Pressure 


both cases, the force is always perpendicular to 
the walls. 


| 1 42 



y 

* 


The air pressure on top of Mount Everest, the 
world’s tallest peak, is very low, making breath- 
ing difficult. Most climbers who attempt to scale 
Everest thus carry oxygen tanks with them. 
Shown here is Jim Whittaker, the first American 
to climb Everest. (Photograph by Galen Rowell/Corbis. Repro- 
duced by permission.) 

tories and of households. Since changes in 
atmospheric pressure have an effect on weather 
patterns, many home indoor-outdoor ther- 
mometers today also include a barometer. 

Pressure and Fluids 

In terms of physics, both gases and liquids are 
referred to as fluids — that is, substances that con- 
form to the shape of their container. Air pressure 
and water pressure are thus specific subjects 
under the larger heading of “fluid pressure.” A 
fluid responds to pressure quite differently than a 
solid does. The density of a solid makes it resist- 
ant to small applications of pressure, but if the 
pressure increases, it experiences tension and, 
ultimately, deformation. In the case of a fluid, 
however, stress causes it to flow rather than to 
deform. 

There are three significant characteristics of 
the pressure exerted on fluids by a container. First 
of all, a fluid in a container experiencing no 
external motion exerts a force perpendicular to 
the walls of the container. Likewise, the con- 
tainer walls exert a force on the fluid, and in 

VDLUME 2: REAL-LIFE PHYSICS 


In each of these three characteristics, it is 
assumed that the container is finite: in other 
words, the fluid has nowhere else to go. Hence, 
the second statement: the external pressure exert- 
ed on the fluid is transmitted uniformly. Note 
that the preceding statement was qualified by the 
term “external”: the fluid itself exerts pressure 
whose force component is equal to its weight. 
Therefore, the fluid on the bottom has much 
greater pressure than the fluid on the top, due to 
the weight of the fluid above it. 

Third, the pressure on any small surface of 
the fluid is the same, regardless of that surface’s 
orientation. In other words, an area of fluid per- 
pendicular to the container walls experiences the 
same pressure as one parallel or at an angle to the 
walls. This may seem to contradict the first prin- 
ciple, that the force is perpendicular to the walls 
of the container. In fact, force is a vector quanti- 
ty, meaning that it has both magnitude and 
direction, whereas pressure is a scalar, meaning 
that it has magnitude but no specific direction. 

REAL-LIFE 
A P P L I C AT I □ N S 

Pascal’s Principle and the 
Hydraulic Press 

The three characteristics of fluid pressure 
described above have a number of implications 
and applications, among them, what is known as 
Pascal’s principle. Like the SI unit of pressure, 
Pascal’s principle is named after Blaise Pascal 
(1623-1662), a French mathematician and physi- 
cist who formulated the second of the three state- 
ments: that the external pressure applied on a 
fluid is transmitted uniformly throughout the 
entire body of that fluid. Pascal’s principle 
became the basis for one of the important 
machines ever developed, the hydraulic press. 

A simple hydraulic press of the variety used 
to raise a car in an auto shop typically consists of 
two large cylinders side by side. Each cylinder 
contains a piston, and the cylinders are connect- 
ed at the bottom by a channel containing fluid. 
Valves control flow between the two cylinders. 
When one applies force by pressing down the pis- 
ton in one cylinder (the input cylinder), this 
yields a uniform pressure that causes output in 

SCIENCE OF EVERYDAY THINGS 



Pressure 


the second cylinder, pushing up a piston that 
raises the car. 

In accordance with Pascal’s principle, the 
pressure throughout the hydraulic press is the 
same, and will always be equal to the ratio 
between force and pressure. As long as that ratio 
is the same, the values of F and A may vary. In the 
case of an auto-shop car jack, the input cylinder 
has a relatively small surface area, and thus, the 
amount of force that must be applied is relative- 
ly small as well. The output cylinder has a rela- 
tively large surface area, and therefore, exerts a 
relatively large force to lift the car. This, com- 
bined with the height differential between the 
two cylinders (discussed in the context of 
mechanical advantage elsewhere in this book), 
makes it possible to lift a heavy automobile with 
a relatively small amount of effort. 

THE HYDRAULIC RAM. The Car 

jack is a simple model of the hydraulic press in 
operation, but in fact, Pascal’s principle has many 
more applications. Among these is the hydraulic 
ram, used in machines ranging from bulldozers 
to the hydraulic lifts used by firefighters and util- 
ity workers to reach heights. In a hydraulic ram, 
however, the characteristics of the input and out- 
put cylinders are reversed from those of a car 
jack. 

The input cylinder, called the master cylin- 
der, has a large surface area, whereas the output 
cylinder (called the slave cylinder) has a small 
surface area. In addition — though again, this is a 
factor related to mechanical advantage rather 
than pressure, per se — the master cylinder is 
short, whereas the slave cylinder is tall. Owing to 
the larger surface area of the master cylinder 
compared to that of the slave cylinder, the 
hydraulic ram is not considered efficient in terms 
of mechanical advantage: in other words, the 
force input is much greater than the force output. 

Nonetheless, the hydraulic ram is as well- 
suited to its purpose as a car jack. Whereas the 
jack is made for lifting a heavy automobile 
through a short vertical distance, the hydraulic 
ram carries a much lighter cargo (usually just one 
person) through a much greater vertical range — 
to the top of a tree or building, for instance. 

Exploiting Pressure Differ- 
ences 

pumps. A pump utilizes Pascal’s princi- 
ple, but instead of holding fluid in a single con- 

SCIENCE DF EVERYDAY THINGS 


tainer, a pump allows the fluid to escape. Specif- 
ically, the pump utilizes a pressure difference, 
causing the fluid to move from an area of higher 
pressure to one of lower pressure. A very simple 
example of this is a siphon hose, used to draw 
petroleum from a car’s gas tank. Sucking on one 
end of the hose creates an area of low pressure 
compared to the relatively high-pressure area of 
the gas tank. Eventually, the gasoline will come 
out of the low-pressure end of the hose. (And 
with luck, the person siphoning will be able to 
anticipate this, so that he does not get a mouth- 
ful of gasoline!) 

The piston pump, more complex, but still 
fairly basic, consists of a vertical cylinder along 
which a piston rises and falls. Near the bottom of 
the cylinder are two valves, an inlet valve through 
which fluid flows into the cylinder, and an outlet 
valve through which fluid flows out of it. On the 
suction stroke, as the piston moves upward, the 
inlet valve opens and allows fluid to enter the 
cylinder. On the downstroke, the inlet valve clos- 
es while the outlet valve opens, and the pressure 
provided by the piston on the fluid forces it 
through the outlet valve. 

One of the most obvious applications of the 
piston pump is in the engine of an automobile. 
In this case, of course, the fluid being pumped is 
gasoline, which pushes the pistons by providing a 
series of controlled explosions created by the 
spark plug’s ignition of the gas. In another vari- 
ety of piston pump — the kind used to inflate a 
basketball or a bicycle tire — air is the fluid being 
pumped. Then there is a pump for water, which 
pumps drinking water from the ground It may 
also be used to remove desirable water from an 
area where it is a hindrance, for instance, in the 
bottom of a boat. 

BERNOULLI’S PRINCIPLE. 

Though Pascal provided valuable understanding 
with regard to the use of pressure for performing 
work, the thinker who first formulated general 
principles regarding the relationship between 
fluids and pressure was the Swiss mathematician 
and physicist Daniel Bernoulli (1700-1782). 
Bernoulli is considered the father of fluid 
mechanics, the study of the behavior of gases and 
liquids at rest and in motion. 

While conducting experiments with liquids, 
Bernoulli observed that when the diameter of a 
pipe is reduced, the water flows faster. This sug- 
gested to him that some force must be acting 

VDLUME 2: REAL-LIFE PHYSICS 


1 43 


Pressure 


| 1 44 


upon the water, a force that he reasoned must 
arise from differences in pressure. Specifically, 
the slower-moving fluid in the wider area of pipe 
had a greater pressure than the portion of the 
fluid moving through the narrower part of the 
pipe. As a result, he concluded that pressure and 
velocity are inversely related — in other words, as 
one increases, the other decreases. 

Hence, he formulated Bernoulli’s principle, 
which states that for all changes in movement, 
the sum of static and dynamic pressure in a fluid 
remain the same. A fluid at rest exerts static pres- 
sure, which is commonly meant by “pressure,” as 
in “water pressure.” As the fluid begins to move, 
however, a portion of the static pressure — pro- 
portional to the speed of the fluid — is converted 
to what is known as dynamic pressure, or the 
pressure of movement. In a cylindrical pipe, stat- 
ic pressure is exerted perpendicular to the surface 
of the container, whereas dynamic pressure is 
parallel to it. 

According to Bernoulli’s principle, the 
greater the velocity of flow in a fluid, the greater 
the dynamic pressure and the less the static pres- 
sure: in other words, slower-moving fluid exerts 
greater pressure than faster-moving fluid. The 
discovery of this principle ultimately made pos- 
sible the development of the airplane. 

As fluid moves from a wider pipe to a nar- 
rower one, the volume of that fluid that moves a 
given distance in a given time period does not 
change. But since the width of the narrower pipe 
is smaller, the fluid must move faster (that is, 
with greater dynamic pressure) in order to move 
the same amount of fluid the same distance in 
the same amount of time. One way to illustrate 
this is to observe the behavior of a river: in a 
wide, unconstricted region, it flows slowly, but if 
its flow is narrowed by canyon walls, then it 
speeds up dramatically. 

Bernoulli’s principle ultimately became the 
basis for the airfoil, the design of an airplane’s 
wing when seen from the end. An airfoil is 
shaped like an asymmetrical teardrop laid on its 
side, with the “fat” end toward the airflow. As air 
hits the front of the airfoil, the airstream divides, 
part of it passing over the wing and part passing 
under. The upper surface of the airfoil is curved, 
however, whereas the lower surface is much 
straighten 

As a result, the air flowing over the top has a 
greater distance to cover than the air flowing 

VDLUME 2: REAL-LIFE PHYSICS 


under the wing. Since fluids have a tendency to 
compensate for all objects with which they come 
into contact, the air at the top will flow faster to 
meet with air at the bottom at the rear end of the 
wing. Faster airflow, as demonstrated by 
Bernoulli, indicates lower pressure, meaning that 
the pressure on the bottom of the wing keeps the 
airplane aloft. 

Buoyancy and Pressure 

One hundred and twenty years before the first 
successful airplane flight by the Wright brothers 
in 1903, another pair of brothers — the Mont- 
golfiers of France — developed another means of 
flight. This was the balloon, which relied on an 
entirely different principle to get off the ground: 
buoyancy, or the tendency of an object immersed 
in a fluid to float. As with Bernoulli’s principle, 
however, the concept of buoyancy is related to 
pressure. 

In the third century b.c., the Greek mathe- 
matician, physicist, and inventor Archimedes (c. 
287-212 B.c.) discovered what came to be known 
as Archimedes’s principle, which holds that the 
buoyant force of an object immersed in fluid is 
equal to the weight of the fluid displaced by the 
object. This is the reason why ships float: because 
the buoyant, or lifting, force of them is less than 
equal to the weight of the water they displace. 

The hull of a ship is designed to displace or 
move a quantity of water whose weight is greater 
than that of the vessel itself. The weight of the 
displaced water — that is, its mass multiplied by 
the downward acceleration caused by gravity — is 
equal to the buoyant force that the ocean exerts 
on the ship. If the ship weighs less than the water 
it displaces, it will float; but if it weighs more, it 
will sink. 

The factors involved in Archimedes’s princi- 
ple depend on density, gravity, and depth rather 
than pressure. However, the greater the depth 
within a fluid, the greater the pressure that push- 
es against an object immersed in the fluid. More- 
over, the overall pressure at a given depth in a 
fluid is related in part to both density and gravi- 
ty, components of buoyant force. 

PRESSURE AND DEPTH. The 

pressure that a fluid exerts on the bottom of its 
container is equal to dgh, where d is density, g the 
acceleration due to gravity, and h the depth of the 
container. For any portion of the fluid, h is equal 
to its depth within the container, meaning that 

SCIENCE DF EVERYDAY THINGS 



This yellow diving suit, called a “newt suit,” is specially designed td withstand the enormous water 
pressure that exists at lower depths of the ocean. (Photograph by Amos Nachoum/Corbis. Reproduced by permission.) 


the deeper one goes, the greater the pressure. 
Furthermore, the total pressure within the fluid 
is equal to dgh + p external , where p external is the pres- 
sure exerted on the surface of the fluid. In a pis- 
ton-and-cylinder assembly, this pressure comes 
from the piston, but in water, the pressure comes 
from the atmosphere. 

In this context, the ocean may be viewed as a 
type of “container.” At its surface, the air exerts 
downward pressure equal to 1 atm. The density 
of the water itself is uniform, as is the downward 
acceleration due to gravity; the only variable, 
then, is h, or the distance below the surface. At 
the deepest reaches of the ocean, the pressure is 
incredibly great — far more than any human 
being could endure. This vast amount of pressure 
pushes upward, resisting the downward pressure 
of objects on its surface. At the same time, if a 
boat’s weight is dispersed properly along its hull, 
the ship maximizes area and minimizes force, 
thus exerting a downward pressure on the surface 
of the water that is less than the upward pressure 
of the water itself. Hence, it floats. 

Pressure and the Human 
Bddy 

air pressure. The Montgolfiers 
used the principle of buoyancy not to float on the 

SCIENCE OF EVERYDAY THINGS 


water, but to float in the sky with a craft lighter 
than air. The particulars of this achievement are 
discussed elsewhere, in the context of buoyancy; 
but the topic of lighter- than -air flight suggests 
another concept that has been alluded to several 
times throughout this essay: air pressure. 

Just as water pressure is greatest at the bot- 
tom of the ocean, air pressure is greatest at the 
surface of the Earth — which, in fact, is at the bot- 
tom of an “ocean” of air. Both air and water pres- 
sure are examples of hydrostatic pressure — the 
pressure that exists at any place in a body of fluid 
due to the weight of the fluid above. In the case 
of air pressure, air is pulled downward by the 
force of Earth’s gravitation, and air along the sur- 
face has greater pressure due to the weight (a 
function of gravity) of the air above it. At great 
heights above Earth’s surface, however, the gravi- 
tational force is diminished, and, thus, the air 
pressure is much smaller. 

In ordinary experience, a person’s body is 
subjected to an impressive amount of pressure. 
Given the value of atmospheric pressure 
discussed earlier, if one holds out one’s 
hand — assuming that the surface is about 20 in 2 
(0.129 m 2 ) — the force of the air resting on it is 
nearly 300 lb (136 kg)! How is it, then, that one’s 

VDLUME 2: REAL-LIFE PHYSICS 


1 4 5 



Pressure 


THE RESPONSE TO CHANGES 


| 1 46 


KEY TERMS 


atmosphere: A measure of pres- 

sure, abbreviated “atm” and equal to the 
average pressure exerted by air at sea level. 
In English units, this is equal to 14.7 
pounds per square inch, and in SI units to 
101,300 pascals. 

bard meter: An instrument for 

measuring atmospheric pressure. 

budyancy: The tendency of an obj ect 

immersed in a fluid to float. 

fluid: Any substance, whether gas or 

liquid, that conforms to the shape of its 
container. 

fluid mechanics: The study of 

the behavior of gases and liquids at rest 
and in motion. 

HYDRDSTATIC PRESSURE: the 

pressure that exists at any place in a body of 
fluid due to the weight of the fluid above. 

pascal: The principle SI or metric 

unit of pressure, abbreviated “Pa” and 
equal to 1 N/m 2 . 

pascal’s principle: A statement, 

formulated by French mathematician and 
physicist Blaise Pascal (1623-1662), which 
holds that the external pressure applied on 
a fluid is transmitted uniformly through- 
out the entire body of that fluid. 

pressure: The ratio of force to sur- 

face area, when force is applied in a direc- 
tion perpendicular to that surface. The for- 
mula for pressure ( p ) is p = FI A, where F is 
force and A the surface area. 


hand is not crushed by all this weight? The rea- 
son is that the human body itself is under pres- 
sure, and that the interior of the body exerts a 
pressure equal to that of the air. 

vdlume z: real-life physics 


in air pressure. The human body is, 
in fact, suited to the normal air pressure of 1 atm, 
and if that external pressure is altered, the body 
undergoes changes that may be harmful or even 
fatal. A minor example of this is the “popping” in 
the ears that occurs when one drives through the 
mountains or rides in an airplane. With changes 
in altitude come changes in pressure, and thus, 
the pressure in the ears changes as well. 

As noted earlier, at higher altitudes, the air 
pressure is diminished, which makes it harder to 
breathe. Because air is a gas, its molecules have a 
tendency to be non-attractive: in other words, 
when the pressure is low, they tend to move away 
from one another, and the result is that a person 
at a high altitude has difficulty getting enough air 
into his or her lungs. Runners competing in the 
1968 Olympics at Mexico City, a town in the 
mountains, had to train in high-altitude environ- 
ments so that they would be able to breathe dur- 
ing competition. For baseball teams competing 
in Denver, Colorado (known as “the Mile-High 
City”), this disadvantage in breathing is compen- 
sated by the fact that lowered pressure and resist- 
ance allows a baseball to move more easily 
through the air. 

If a person is raised in such a high-altitude 
environment, of course, he or she becomes used 
to breathing under low air pressure conditions. 
In the Peruvian Andes, for instance, people spend 
their whole lives at a height more than twice as 
great as that of Denver, but a person from a low- 
altitude area should visit such a locale only after 
taking precautions. At extremely great heights, of 
course, no human can breathe: hence airplane 
cabins are pressurized. Most planes are equipped 
with oxygen masks, which fall from the ceiling if 
the interior of the cabin experiences a pressure 
drop. Without these masks, everyone in the cabin 
would die. 

bldod pressure. Another as- 
pect of pressure and the human body is blood 
pressure. Just as 20/20 vision is ideal, doctors rec- 
ommend a target blood pressure of “120 over 
80” — but what does that mean? When a person’s 
blood pressure is measured, an inflatable cuff is 
wrapped around the upper arm at the same level 
as the heart. At the same time, a stethoscope is 
placed along an artery in the lower arm to mon- 
itor the sound of the blood flow. The cuff is 
inflated to stop the blood flow, then the pressure 

SCIENCE DF EVERYDAY THINGS 



is released until the blood just begins flowing 
again, producing a gurgling sound in the stetho- 
scope. 

The pressure required to stop the blood flow 
is known as the systolic pressure, which is equal 
to the maximum pressure produced by the heart. 
After the pressure on the cuff is reduced until the 
blood begins flowing normally — which is reflect- 
ed by the cessation of the gurgling sound in the 
stethoscope — the pressure of the artery is meas- 
ured again. This is the diastolic pressure, or the 
pressure that exists within the artery between 
strokes of the heart. For a healthy person, systolic 
pressure should be 120 torr, and diastolic pres- 
sure 80 torr. 

WHERE TD LEARN MDRE 

“Atmospheric Pressure: The Force Exerted by the Weight of 
Air” (Web site), <http://kids.earth.nasa.gov/archive/ 
air_pressure/> (April 7, 2001). 


Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Blood Pressure” (Web site), <http://www.mckinley.uiuc. 
edu/health-info/dis-cond/bloodpr/bloodpr.html> 
(April 7, 2001). 

Clark, John Owen Edward. The Atmosphere. New York: 
Gloucester Press, 1992. 

Cobb, Allan B. Super Science Projects About Oceans. New 
York: Rosen, 2000. 

“The Physics of Underwater Diving: Pressure Lesson” 

(Web site), <http://www.uncwil.edu/nurc/aquarius/ 
lessons/pressure. html> (April 7, 2001). 

Provenzo, Eugene F. and Asterie Baker Provenzo. 47 
Easy-to-Do Classic Experiments. Illustrations by Peter 
A. Zorn, Jr. New York: Dover Publications, 1989. 

“Understanding Air Pressure” USA Today (Web site). 
<http://www.usatoday.com/weather/wbarocx.html> 
(April 7, 2001). 

Zubrowski, Bernie. Balloons: Building and Experimenting 
with Inflatable Toys. Illustrated by Roy Doty. New 
York: Morrow Junior Books, 1990. 


Pressure 


1 47 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


ELASTICITY 


C □ N C E PT 

Unlike fluids, solids do not respond to outside 
force by flowing or easily compressing. The term 
elasticity refers to the manner in which solids 
respond to stress, or the application of force over 
a given unit area. An understanding of elastici- 
ty — a concept that carries with it a rather exten- 
sive vocabulary of key terms — helps to illuminate 
the properties of objects from steel bars to rubber 
bands to human bones. 

H □ W IT WDRKS 

Characteristics of a Solid 

A number of parameters distinguish solids from 
fluids, a term that in physics includes both gases 
and liquids. Solids possess a definite volume and 
a definite shape, whereas gases have neither; liq- 
uids have no definite shape. 

At the molecular level, particles of solids 
tend to be precise in their arrangement and close 
to one another. Liquid molecules are close in 
proximity (though not as much so as solid mole- 
cules), and their arrangement is random, while 
gas molecules are both random in arrangement 
and far removed in proximity. Gas molecules are 
extremely fast-moving, and exert little or no 
attraction toward one another. Liquid molecules 
move at moderate speeds and exert a moderate 
attraction, but solid particles are slow-moving, 
and have a strong attraction to one another. 

One of several factors that distinguishes 
solids from fluids is their relative response to 
pressure. Gases tend to be highly compressible, 
meaning that they respond well to pressure. Liq- 
uids tend to be noncompressible, yet because of 
their fluid characteristics, they experience exter- 

VDLUME 2: REAL-LIFE PHYSICS 


nal pressure uniformly. If one applies pressure to 
a quantity of water in a closed container, the 
pressure is equal everywhere in the water. By con- 
trast, if one places a champagne glass upright in 
a vise and applies pressure until it breaks, chances 
are that the stem or the base of the glass will be 
unaffected, because the pressure is not distrib- 
uted equally throughout the glass. 

If the surface of a solid is disturbed, it will 
resist, and if the force of the disturbance is suffi- 
ciently strong, it will deform — for instance, when 
a steel plate begins to bend under pressure. This 
deformation will be permanent if the force is 
powerful enough, as in the above example of the 
glass in a vise. By contrast, when the surface of a 
fluid is disturbed, it tends to flow. 

Types of Stress 

Deformation occurs as a result of stress, whether 
that stress be in the form of tension, compres- 
sion, or shear. Tension occurs when equal and 
opposite forces are exerted along the ends of an 
object. These operate on the same line of action, 
but away from each other, thus stretching the 
object. A perfect example of an object under ten- 
sion is a rope in the middle of a tug-of-war com- 
petition. The adjectival form of “tension” is “ten- 
sile”: hence the term “tensile stress,” which will be 
discussed later. 

Earlier, stress was defined as the application 
of force over a given unit area, and in fact, the 
formula for stress can be written as FI A, where F 
is force and A area. This is also the formula for 
pressure, though in order for an object to be 
under pressure, the force must be applied in a 
direction perpendicular to — and in the same 
direction as — its surface. The one form of stress 

SCIENCE □ F EVERYDAY THINGS 



that clearly matches these parameters is compres- 
sion, produced by the action of equal and oppo- 
site forces, whose effect is to reduce the length of 
a material. Thus compression (for example, 
crushing an aluminum can in one’s hand) is both 
a form of stress and a form of pressure. 

Note that compression was defined as reduc- 
ing length, yet the example given involved a 
reduction in what most people would call the 
“width” or diameter of the aluminum can. In 
fact, width and height are the same as length, for 
the purposes of most discussions in physics. 
Length is, along with time, mass, and electric cur- 
rent, one of the fundamental units of measure 
used to express virtually all other physical quan- 
tities. Width and height are simply length 
expressed in terms of other planes, and within 
the subject of elasticity, it is not important to dis- 
tinguish between these varieties of length. (By 
contrast, when discussing gravitational attrac- 
tion — which is always vertical — it is obviously 
necessary to distinguish between “vertical 
length,” or height, and horizontal length.) 

The third variety of stress is shear, which 
occurs when a solid is subjected to equal and 
opposite forces that do not act along the same 
line, and which are parallel to the surface area of 
the object. If a thick hardbound book is lying flat, 
and a person places a finger on the spine and 
pushes the front cover away from the spine so 
that the covers and pages no longer constitute 
parallel planes, this is an example of shear. Stress 
resulting from shear is called shearing stress. 

Hdqke’s Law and Elastic 
Limit 

To sum up the three varieties of stress, tension 
stretches an object, compression shrinks it, and 
shear twists it. In each case, the object is 
deformed to some degree. This deformation is 
expressed in terms of strain, or the ratio between 
change in dimension and the original dimen- 
sions of the object. The formula for strain is 
8 LIL 0 , where 8 L is the change in length (8, the 
Greek letter delta, means “change” in scientific 
notation) and L a the original length. 

Hooke’s law, formulated by English physicist 
Robert Hooke (1635-1703), relates strain to 
stress. Hooke’s law can be stated in simple terms 
as “the strain is proportional to the stress,” and 
can also be expressed in a formula, F = ks, where 
F is the applied force, s, the resulting change in 

SCIENCE □ E EVERYDAY THINGS 


dimension, and k, a constant whose value is relat- 
ed to the nature and size of the object under 
stress. The harder the material, the higher the 
value of k; furthermore, the value of k is directly 
proportional to the object’s cross-sectional area 
or thickness. 

The elastic limit of a given solid is the maxi- 
mum stress to which it can be subjected without 
experiencing permanent deformation. Elastic 
limit will be discussed in the context of several 
examples below; for now, it is important merely 
to know that Hooke’s law is applicable only as 
long as the material in question has not reached 
its elastic limit. The same is true for any modulus 
of elasticity, or the ratio between a particular 
type of applied stress and the strain that results. 
(The term “modulus,” whose plural is “moduli,” 
is Latin for “small measure.”) 

Moduli of Elasticity 

In cases of tension or compression, the modulus 
of elasticity is Young’s modulus. Named after 
English physicist Thomas Young (1773-1829), 
Young’s modulus is simply the ratio between FI A 
and 8 LIL a — in other words, stress divided by 
strain. There are also moduli describing the 
behavior of objects exposed to shearing stress 
(shear modulus), and of objects exposed to com- 
pressive stress from all sides (bulk modulus). 

Shear modulus is the relationship of shear- 
ing stress to shearing strain. This can be 
expressed as the ratio between FI A and 0. The 
latter symbol, the Greek letter phi, stands for the 
angle of shear — that is, the angle of deformation 
along the sides of an object exposed to shearing 
stress. The greater the amount of surface area A, 
the less that surface will be displaced by the force 
F. On the other hand, the greater the amount of 
force in proportion to A, the greater the value of 
0, which measures the strain of an object 
exposed to shearing stress. (The value of 0, how- 
ever, will usually be well below 90°, and certain- 
ly cannot exceed that magnitude.) 

With tensile and compressive stress, A is a 
surface perpendicular to the direction of applied 
force, but with shearing stress, A is parallel to F. 
Consider again the illustration used above, of a 
thick hardbound book lying flat. As noted, when 
one pushes the front cover from the side so that 
the covers and pages no longer constitute parallel 
planes, this is an example of shear. If one pulled 
the spine and the long end of the pages away 

VDLUME Z : REAL-LIFE PHYSICS 


ELASTICITY 


1 49 



The machine pictured here rolls over steel in order to bend it into pipes. Because of its elastic 
nature, steel can be bent without breaking. (Photograph by Vince Streano/Corbis. Reproduced by permission.) 


| 1 5 □ 


from one another, that would be tensile stress, 
whereas if one pushed in on the sides of the pages 
and spine, that would be compressive stress. 
Shearing stress, by contrast, would stress only the 
front cover, which is analogous to A for any 
object under shearing stress. 

The third type of elastic modulus is bulk 
modulus, which occurs when an object is sub- 
jected to compression from all sides — that is, vol- 
ume stress. Bulk modulus is the relationship of 
volume stress to volume strain, expressed as the 
ratio between FI A and 8 VIV Q , where SU is the 
change in volume and V a is the original volume. 

REAL-LI F E 
A P P L I C AT I □ N S 

Elastic and Plastic Deforma- 
tion 

As noted earlier, the elastic limit is the maximum 
stress to which a given solid can be subjected 
without experiencing permanent deformation, 
referred to as plastic deformation. Plastic defor- 
mation describes a permanent change in shape 
or size as a result of stress; by contrast, elastic 
deformation is only a temporary change in 
dimension. 

VDLUME 2: REAL-LIFE PHYSICS 


A classic example of elastic deformation, and 
indeed, of highly elastic behavior, is a rubber 
band: it can be deformed to a length many times 
its original size, but upon release, it returns to its 
original shape. Examples of plastic deformation, 
on the other hand, include the bending of a steel 
rod under tension or the breaking of a glass 
under compression. Note that in the case of the 
steel rod, the object is deformed without ruptur- 
ing — that is, without breaking or reducing to 
pieces. The breaking of the glass, however, is 
obviously an instance of rupturing. 

Metals and Elasticity 

Metals, in fact, exhibit a number of interesting 
characteristics with regard to elasticity. With the 
notable exception of cast iron, metals tend to 
possess a high degree of ductility, or the ability to 
be deformed beyond their elastic limits without 
experiencing rupture. Up to a certain point, the 
ratio of tension to elongation for metals is high: 
in other words, a high amount of tension pro- 
duces only a small amount of elongation. Beyond 
the elastic limit, however, the ratio is much lower: 
that is, a relatively small amount of tension pro- 
duces a high degree of elongation. 

Because of their ductility, metals are highly 
malleable, and, therefore, capable of experienc- 

SCIENCE OF EVERYDAY THINGS 



Elasticity 



Rubber bands, like the ones shown here formed into a ball, are a classic example of elastic defor- 
m ati o n . (Photograph by Matthew Klein/Corbis. Reproduced by permission.) 


mg mechanical deformation through metallurgi- 
cal processes, such as forging, rolling, and extru- 
sion. Cold extrusion involves the application of 
high pressure — that is, a high bulk modulus — to 
a metal without heating it, and is used on mate- 
rials such as tin, zinc, and copper to change their 
shape. Hot extrusion, on the other hand, involves 
heating a metal to a point of extremely high mal- 
leability, and then reshaping it. Metals may also 
be melted for the purposes of casting, or pouring 
the molten material into a mold. 

ultimate strength. The ten- 
sion that a material can withstand is called its 
ultimate strength, and due to their ductile prop- 
erties, most metals possess a high value of ulti- 
mate strength. It is possible, however, for a metal 
to break down due to repeated cycles of stress 
that are well below the level necessary to rupture 
it. This occurs, for instance, in metal machines 
such as automobile engines that experience a 
high frequency of stress cycles during operation. 

The high ultimate strength of metals, both in 
tension and compression, makes them useful in a 
number of structural capacities. Steel has an ulti- 
mate compressive strength 25 times as great as 
concrete, and an ultimate tensile strength 250 
times as great. For this reason, when concrete is 
poured for building bridges or other large struc- 

SCIENCE DF EVERYDAY THINGS 


tures, steel rods are inserted in the concrete. 
Called “rebar” (for “reinforced bars”), the steel 
rods have ridges along them in order to bond 
more firmly with the concrete as it dries. As a 
result, reinforced concrete has a much greater 
ability than plain concrete to withstand tension 
and compression. 

Steel Bars and Rubber 
Bands Under Stress 

CRYSTALLINE MATERIALS. Metals 

are crystalline materials, meaning that they are 
composed of solids called crystals. Particles of 
crystals are highly ordered, with a definite geo- 
metric arrangement repeated in all directions, 
rather like a honeycomb. (It should be noted, 
however, that the crystals are not necessarily as 
uniform in size as the “cells” of the honeycomb.) 
The atoms of a crystal are arranged in orderly 
rows, bound to one another by strongly attractive 
forces that act like microscopic springs. 

Just as a spring tends to return to its original 
length, the highly attractive atoms in a steel bar, 
when it is stretched, tend to restore it to its orig- 
inal dimensions. Likewise, it takes a great deal of 
force to pull apart the atoms. When the metal is 
subjected to plastic deformation, the atoms move 

VDLUME 2: REAL-LIFE PHYSICS 


1 5 1 



Elasticity 


| 1 5Z 



A HUMAN BONE HAS A GREATER “ULTIMATE STRENGTH” 

than that OF cgncrete. (Ecoscene/ Corbis. Reproduced by per- 
mission.) 

to new positions and form new bonds. The 
atoms are incapable of forming bonds; however, 
when the metal has been subjected to stress 
exceeding its ultimate strength, at that point, the 
metal breaks. 

The crystalline structure of metal influences 
its behavior under high temperatures. Heat caus- 
es atoms to vibrate, and in the case of metals, this 
means that the “springs” are stretching and com- 
pressing. As temperature increases, so do the 
vibrations, thus increasing the average distance 
between atoms. For this reason, under extremely 
high temperature, the elastic modulus of the 
metal decreases, and the metal becomes less 
resistant to stress. 

POLYMERS AND ELASTOM- 
ERS. Rubber is so elastic in behavior that in 
everyday life, the term “elastic” is most often used 
for objects containing rubber: the waistband on a 
pair of underwear, for instance. The long, thin 
molecules of rubber, which are arranged side-by- 
side, are called “polymers,” and the super-elastic 
polymers in rubber are called “elastomers.” The 
chemical bonds between the atoms in a polymer 

VDLUME 2: REAL-LIFE PHYSICS 


are flexible, and tend to rotate, producing kinks 
along the length of the molecule. 

When a piece of rubber is subjected to ten- 
sion, as, for instance, if one pulls a rubber band 
by the ends, the kinks and loops in the elas- 
tomers straighten. Once the stress is released, 
however, the elastomers immediately return to 
their original shape. The more “kinky” the poly- 
mers, the higher the elastic modulus, and hence, 
the more capable the item is of stretching and 
rebounding. 

It is interesting to note that steel and rubber, 
materials that are obviously quite different, are 
both useful in part for the same reason: their 
high elastic modulus when subjected to tension, 
and their strength under stress. But a rubber 
band exhibits behaviors under high temperatures 
that are quite different from that of a metal: 
when heated, rubber contracts. It does so quite 
suddenly, in fact, suggesting that the added ener- 
gy of the heat allows the bonds in the elastomers 
to begin rotating again, thus restoring the kinked 
shape of the molecules. 

Bdnes 

The tensile strength in bone fibers comes from 
the protein collagen, while the compressive 
strength is largely due to the presence of inor- 
ganic (non-living) salt crystals. It may be hard to 
believe, but bone actually has an ultimate 
strength — both in tension and compression — 
greater than that of concrete! 

The ultimate strength of most materials is 
rendered in factors of 10 s N/m 2 — that is, 
100,000,000 newtons (the metric unit of force) 
per square meter. For concrete under tensile 
stress, the ultimate strength is 0.02, whereas for 
bone, it is 1.3. Under compressive stress, the val- 
ues are 0.2 and 1.7, respectively. In fact, the ulti- 
mate tensile strength of bone is close to that of 
cast iron (1.7), though the ultimate compressive 
strength of cast iron (5.5) is much higher than 
for bone. 

Even with these figures, it may be hard to 
understand how bone can be stronger than con- 
crete, but that is largely because the volume of 
concrete used in most situations is much greater 
than the volume of any bone in the body of a 
human being. By way of explanation, consider a 
piece of concrete no bigger than a typical bone: 
under relatively small amounts of stress, it would 
crumble. 

SCIENCE DF EVERYDAY THINGS 



Elasticity 


KEY TERMS 


angle of shear: The angle of 

deformation on the sides of an object 
exposed to shearing stress. Its symbol is <j) 
(the Greek letter phi), and its value will 
usually be well below 90°. 

bulk modulus: The modulus of 

elasticity for a material subjected to com- 
pression on all surfaces — that is, volume 
stress. Bulk modulus is the relationship of 
volume stress to volume strain, expressed 
as the ratio between FI A and dV/Vo, where 
dV is the change in volume and Vo is the 
original volume. 

compression: A form of stress 

produced by the action of equal and oppo- 
site forces, whose effect is to reduce the 
length of a material. Compression is a form 
of pressure. When compressive stress is 
applied to all surfaces of a material, this is 
known as volume stress. 

ductility: A property whereby a 

material is capable of being deformed far 
beyond its elastic limit without experienc- 
ing rupture — that is, without breaking. 
Most metals other than cast iron are high- 
ly ductile. 

elastic defdrmatidn: A tempo- 

rary change in shape or size experienced by 
a solid subjected to stress. Elastic deforma- 
tion is thus less severe than plastic defor- 
mation. 

elastic limit: The maximum stress 

to which a given solid can be subjected 
without experiencing plastic deforma- 
tion — that is, without being permanently 
deformed. 

elasticity: The response of solids to 

stress. 


h □ □ k e ’ s law: A principle of elastic- 

ity formulated by English physicist Robert 
Hooke (1635-1703), who discovered that 
strain is proportional to stress. Hooke’s law 
can be written as a formula, F = ks, where 
F is the applied force, s the resulting change 
in dimension, and k a constant whose value 
is related to the nature and size of the 
object being subjected to stress. Hooke’s 
law applies only when the elastic limit has 
not been exceeded. 

length: In discussions of elasticity, 

“length” refers to an object’s dimensions on 
any given plane, thus, it can be used not 
only to refer to what is called length in 
everyday language, but also to width or 
height. 

MODULUS GF ELASTICITY: The 

ratio between a type of applied stress (that 
is, tension, compression, and shear) and 
the strain that results in the object to which 
stress has been applied. Elastic moduli — 
including Young’s modulus, shearing mod- 
ulus, and bulk modulus — are applicable 
only as long as the object’s elastic limit has 
not been reached. 

plastic defdrmatidn: A perma- 

nent change in shape or size experienced 
by a solid subjected to stress. Plastic defor- 
mation is thus more severe than elastic 
deformation. 

pressure: The ratio of force to sur- 

face area, when force is applied in a direc- 
tion perpendicular to, and in the same 
direction as, that surface. 


1 53 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 



Elasticity 


KEY TERMS continued 


shear: A form of stress resulting 

from equal and opposite forces that do not 
act along the same line. If a thick hard- 
bound book is lying flat, and one pushes 
the front cover from the side so that the 
covers and pages no longer constitute par- 
allel planes, this is an example of shear. 

shear modulus: The modulus of 

elasticity for an object exposed to shearing 
stress. It is expressed as the ratio between 
FI A and 0, where 0 (the Greek letter phi) 
stands for the angle of shear. 

strain: The ratio between the change 

in dimension experienced by an object that 
has been subjected to stress, and the origi- 
nal dimensions of the object. The formula 
for strain is d LIL a , where dL is the change 
in length and L a the original length. 
Hooke’s law, as well as the various moduli 
of elasticity, relates strain to stress. 

stress: In general terms, stress is any 

attempt to deform a solid. Types of stress 
include tension, compression, and shear. 
More specifically, stress is the ratio of force 
to unit area, FI A , where F is force and A 


area. Thus, it is similar to pressure, and 
indeed, compression is a form of pressure. 

tension: A form of stress produced 

by a force which acts to stretch a material. 
The adjectival form of “tension” is “ten- 
sile”: hence the terms “tensile stress” and 
“tensile strain.” 

ultimate strength: The tension 

that a material can withstand without rup- 
turing. Due to their high levels of ductility, 
most metals have a high value of ultimate 
strength. 

volume stress: The stress that 

occurs in a material when it is subjected to 
compression from all sides. The modus of 
elasticity for volume stress is the bulk mod- 
ulus. 

young’s modulus: A modulus of 

elasticity describing the relationship 
between stress to strain for objects under 
either tension or compression. Named 
after English physicist Thomas Young 
(1773-1829), Young’s modulus is simply 
the ratio between FI A and 8 LIL a — in other 
words, stress divided by strain. 


WHERE TE) LEARN M El R E 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Dictionary of Metallurgy" Steelmill.com: The Polish Steel 
Industry Directory (Web site). <http://www.steelmill. 
com/DICTIONARY/Diction-ary.htm> (April 9, 
2001). 

“Engineering Processes.” eFunda.com (Web site). 

<http://www.efunda.com/processes/processes_home/ 
process.cfm> (April 9, 2001). 


Gibson, Gary. Making Shapes. Illustrated by Tony Ken- 
yon. Brookfield, CT: Copper Beech Books, 1996. 

“Glossary of Materials Testing Terms” (Web site). 

<http://www.instron.com/apps/glossary> (April 9, 
2001 ). 

Goodwin, Peter H. Engineering Projects for Young Scien- 
tists. New York: Franklin Watts, 1987. 

Johnston, Tom. The Forces with You! Illustrated by Sarah 
Pooley. Milwaukee, WI: Gareth Stevens Publishing, 
1988. 


| 1 54 


VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



SCIENCE CDF EVERYDAY THINGS 

REAL-LIFE PHYSICS 

W □ R K AND ENERGY 

MECHANICAL ADVANTAGE AND 
SIMPLE MACHINES 

ENERGY 


1 55 




MECHANICAL 
ADVANTAGE AND 
SIMPLE MACHINES 


C □ N C E PT 

When the term machine is mentioned, most peo- 
ple think of complex items such as an automo- 
bile, but, in fact, a machine is any device that 
transmits or modifies force or torque for a spe- 
cific purpose. Typically, a machine increases 
either the force of the person operating it — an 
aspect quantified in terms of mechanical advan- 
tage — or it changes the distance or direction 
across which that force can be operated. Even a 
humble screw is a machine; so too is a pulley, and 
so is one of the greatest machines ever invented: 
the wheel. Virtually all mechanical devices are 
variations on three basic machines: the lever, the 
inclined plane, and the hydraulic press. From 
these three, especially the first two, arose literally 
hundreds of machines that helped define history, 
and which still permeate daily life. 

H □ W IT WORKS 

Machines and Classical 
M ECHANICS 

There are four known types of force in the uni- 
verse: gravitational, electromagnetic, weak 
nuclear, and strong nuclear. This was the order in 
which the forces were identified, and the number 
of machines that use each force descends in the 
same order. The essay that follows will make lit- 
tle or no reference to nuclear-powered machines. 
Somewhat more attention will be paid to electri- 
cal machines; however, to trace in detail the 
development of forces in that context would 
require a new and somewhat cumbersome 
vocabulary. 

SCIENCE □ E EVERYDAY THINGS 


Instead, the machines presented for consid- 
eration here depend purely on gravitational force 
and the types of force explainable purely in a 
gravitational framework. This is the realm of 
classical physics, a term used to describe the stud- 
ies of physicists from the time of Galileo Galilei 
(1564-1642) to the end of the nineteenth centu- 
ry. During this era, physicists were primarily con- 
cerned with large-scale interactions that were 
easily comprehended by the senses, as opposed to 
the atomic behaviors that have become the sub- 
ject of modern physics. 

Late in the classical era, the Scottish physicist 
James Clerk Maxwell (1831-1879) — building on 
the work of many distinguished predecessors — 
identified electromagnetic force. For most of the 
period, however, the focus was on gravitational 
force and mechanics, or the study of matter, 
motion, and forces. Likewise, the majority of 
machines invented and built during most of the 
classical period worked according to the mechan- 
ical principles of plain gravitational force. 

This was even true to some extent with the 
steam engine, first developed late in the seven- 
teenth century and brought to fruition by Scot- 
land’s James Watt (1736-1819.) Yet the steam 
engine, though it involved ordinary mechanical 
processes in part, represented a new type of 
machine, which used thermal energy. This is also 
true of the internal-combustion engine; yet both 
steam- and gas-powered engines to some extent 
borrowed the structure of the hydraulic press, 
one of the three basic types of machine. Then 
came the development of electronic power, 
thanks to Thomas Edison (1847-1931) and oth- 
ers, and machines became increasingly divorced 
from basic mechanical laws. 

VDLUME 2: REAL-LIFE PHYSICS 


1 57 



Mechanical 
Advantage 
and Simple 
Machines 



The lever, like this hydroelectric engine lever, 

IS A SIMPLE MACHINE THAT PERFECTLY ILLUSTRATES THE 

concept of mechanical advantage. (Photograph by E.O. 
Hoppe/Corbis. Reproduced by permission.) 

The heyday of classical mechanics — when 
classical studies in mechanics represented the 
absolute cutting edge of experimentation — was 
in the period from the beginning of the seven- 
teenth century to the beginning of the nine- 
teenth. One figure held a dominant position in 
the world of physics during those two centuries, 
and indeed was the central figure in the history of 
physics between Galileo and Albert Einstein 
(1879-1955). This was Sir Isaac Newton (1642- 
1727), who discerned the most basic laws of 
physical reality — laws that govern everyday life, 
including the operation of simple machines. 

Newton and his principles are essential to 
the study that follows, but one other figure 
deserves “equal billing”: the Greek mathemati- 
cian, physicist, and inventor Archimedes (c. 287- 
212 b.c.). Nearly 2,000 years before Newton, 
Archimedes explained and improved a number 
of basic machines, most notably the lever. 
Describing the powers of the lever, he is said to 
have promised, “Give me a lever long enough and 
a place to stand, and I will move the world.” This 
he demonstrated, according to one story, by 
moving a fully loaded ship single-handedly with 
the use of a lever, while remaining seated some 
distance away. 


Mechanical Advantage 

A common trait runs through all forms of 
machinery: mechanical advantage, or the ratio of 
force output to force input. In the case of the 
lever, a simple machine that will be discussed in 
detail below, mechanical advantage is high. In 
some machines, however, mechanical advantage 
is actually less than 1 , meaning that the resulting 
force is less than the applied force. 

This does not necessarily mean that the 
machine itself has a flaw; on the contrary, it can 
mean that the machine has a different purpose 
than that of a lever. One example of this is the 
screw: a screw with a high mechanical advan- 
tage — that is, one that rewarded the user’s input 
of effort by yielding an equal or greater output — 
would be useless. In this case, mechanical advan- 
tage could only be achieved if the screw backed 
out from the hole in which it had been placed, 
and that is clearly not the purpose of a screw. 

Here a machine offers an improvement in 
terms of direction rather than force; likewise 
with scissors or a fishing rod, both of which will 
be discussed below, an improvement with regard 
to distance or range of motion is bought at the 
expense of force. In these and many more cases, 
mechanical advantage alone does not measure 
the benefit. Thus, it is important to keep in mind 
what was previously stated: a machine either 
increases force output, or changes the force’s dis- 
tance or direction of operation. 

Most machines, however, work best when 
mechanical advantage is maximized. Yet me- 
chanical advantage — whether in theoretical 
terms or real-life instances — can only go so high, 
because there are factors that limit it. For one 
thing, the operator must give some kind of input 
to yield an output; furthermore, in most situa- 
tions friction greatly diminishes output. Hence, 
in the operation of a car, for instance, one-quar- 
ter of the vehicle’s energy is expended simply on 
overcoming the resistance of frictional forces. 

For centuries, inventors have dreamed of 
creating a mechanism with an almost infinite 
mechanical advantage. This is the much-sought- 
after “perpetual motion machine,” that would 
only require a certain amount of initial input; 
after that, the machine would simply run on its 
own forever. As output compounded over the 
years, its ratio to input would become so high 
that the figure for mechanical advantage would 
approach infinity. 


1 5B 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



A number of factors, most notably the exis- 
tence of friction, prevent the perpetual motion 
machine from becoming anything other than a 
pipe dream. In outer space, however, the near- 
absence of friction makes a perpetual motion 
machine viable: hence, a space probe launched 
from Earth can travel indefinitely unless or until 
it enters the gravitational field of some other 
body in deep space. 

The concept of a perpetual motion machine, 
at least on Earth, is only an idealization; yet ide- 
alization does have its place in physics. Physicists 
discuss most concepts in terms of an idealized 
state. For instance, when illustrating the acceler- 
ation due to gravity experienced by a body in free 
fall, it is customary to treat such an event as 
though it were taking place under conditions 
divorced from reality. To consider the effects of 
friction, air resistance, and other factors on the 
body’s fall would create an impossibly complicat- 
ed problem — yet real-world situations are just 
that complicated. 

In light of this tendency to discuss physical 
processes in idealized terms, it should be noted 
that there are two types of mechanical advantage: 
theoretical and actual. Efficiency, as applied to 
machines in its most specific scientific sense, is 
the ratio of actual to theoretical mechanical 
advantage. This in some ways resembles the for- 
mula for mechanical advantage itself: once again, 
what is being measured is the relationship 
between “output” (the real behavior of the 
machine) and “input” (the planned behavior of 
the machine). 

As with other mechanical processes, the 
actual mechanical advantage of a machine is a 
much more complicated topic than the theoreti- 
cal mechanical advantage. The gulf between the 
two, indeed, is enormous. It would be almost 
impossible to address the actual behavior of 
machines within an environment framework 
that includes complexities such as friction. 

Each real-world framework — that is, each 
physical event in the real world — is just a bit dif- 
ferent from every other one, due to the many 
varieties of factors involved. By contrast, the ide- 
alized machines of physics problems behave 
exactly the same way in one imaginary situation 
after another, assuming outside conditions are 
the same. Therefore, the only form of mechanical 
advantage that a physicist can easily discuss is 
theoretical. For that reason, the term “efficiency” 


will henceforth be used as a loose synonym for 
mechanical advantage — even though the techni- 
cal definition is rather different. 

Types of Machines 

The term “simple machine” is often used to 
describe the labor-saving devices known to the 
ancient world, most of which consisted of only 
one or two essential parts. Historical sources vary 
regarding the number of simple machines, but 
among the items usually listed are levers, pulleys, 
winches, wheels and axles, inclined planes, 
wedges, and screws. The list, though long, can 
actually be reduced to just two items: levers and 
inclined planes. All the items listed after the lever 
and before the inclined plane — including the 
wheel and axle — are merely variations on the 
lever. The same goes for the wedge and the screw, 
with regard to the inclined plane. 

In fact, all machines are variants on three 
basic devices: the lever, the inclined plane, and 
the hydraulic press. Each transmits or modifies 
force or torque, producing an improvement in 
force, distance, or direction. The first two, which 
will receive more attention here, share several 
aspects not true of the third. First of all, the lever 
and the inclined plane originated at the begin- 
ning of civilization, whereas the hydraulic press is 
a much more recent invention. 

The lever appeared as early as 5000 b.c. in 
the form of a simple balance scale, and within a 
few thousand years, workers in the Near East and 
India were using a crane-like lever called the 
shaduf to lift containers of water. The shaduf, 
introduced in Mesopotamia in about 3000 b.c., 
consisted of a long wooden pole that pivoted on 
two upright posts. At one end of the lever was a 
counterweight, and at the other a bucket. The 
operator pushed down on the pole to fill the 
bucket with water, and then used the counter- 
weight to assist in lifting the bucket. 

The inclined plane made its appearance in 
the earliest days of civilization, when the Egyp- 
tians combined it with rollers in the building of 
their monumental structures, the pyramids. 
Modern archaeologists generally believe that 
Egyptian work gangs raised the huge stone 
blocks of the pyramids through the use of slop- 
ing earthen ramps. These were most probably 
built up alongside the pyramid itself, and then 
removed when the structure was completed. 


Mechanical 
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and Simple 
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SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


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Mechanical 
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The hydraulic press, like the lift holding up this car in a repair shop, is a relatively recent inven- 
tion that is used in many MODERN devices, from car jacks to toilets. (Photograph by Charles E. Rotkin/Corbis. Repro- 
duced by permission.) 


| 1 SD 


In contrast to the distant origins of the other 
two machines, the hydraulic press seems like a 
mere youngster. Also, the first two clearly arose as 
practical solutions first: by the time Archimedes 
achieved a conceptual understanding of these 
machines, they had been in use a long, long time. 
The hydraulic press, on the other hand, first 
emerged from the theoretical studies of the bril- 
liant French mathematician and physicist Blaise 
Pascal (1623-1662.) Nearly 150 years passed 
before the English inventor Joseph Bramah 
(1748-1814) developed a workable hydraulic 
press in 1796, by which time Watt had already 
introduced his improved steam engine. The 
Industrial Revolution was almost underway. 

REAL-LI F E 
A P P L I C AT ID N S 

The Lever 

In its most basic form, the lever consists of a rigid 
bar supported at one point, known as the ful- 
crum. One of the simplest examples of a lever is 
a crowbar, which one might use to move a heavy 
object, such as a rock. In this instance, the ful- 
crum could be the ground, though a more rigid 

vdlume z: real-life physics 


“artificial” fulcrum (such as a brick) would prob- 
ably be more effective. 

As the operator of the crowbar pushes down 
on its long shaft, this constitutes an input of 
force, variously termed applied force, effort force, 
or merely effort. Newtons third law of motion 
shows that there is no such thing as an unpaired 
force in the universe: every input of force in one 
area will yield an output somewhere else. In this 
case, the output is manifested by dislodging the 
stone — that is, the output force, resistance force, 
or load. 

Use of the lever gives the operator much 
greater lifting force than that available to a per- 
son who tried to lift with only the strength of his 
or her own body. Like all machines, the lever 
links input to output, harnessing effort to yield 
beneficial results — in this case, by translating the 
input effort into the output effort of a dislodged 
stone. Note, however, the statement at the begin- 
ning of this paragraph: proper use of a lever actu- 
ally gives a person much greater force than he or 
she would possess unaided. How can this be? 

There is a close relationship between the 
behavior of the lever and the concept of torque, 
as, for example, the use of a wrench to remove a 
lug nut. A wrench, in fact, is a sort of lever (Class 

SCIENCE OF EVERYDAY THINGS 


I — a distinction that will be explored below.) In 
any object experiencing torque, the distance from 
the pivot point (the lug nut, in this case), to the 
area where force is being applied is called the 
moment arm. On the wrench, this is the distance 
from the lug nut to the place where the operator 
is pushing on the wrench handle. Torque is the 
product of force multiplied by moment arm, and 
the greater the torque, the greater the tendency of 
the object to be put into rotation. As with 
machines in general, the greater the input, the 
greater the output. 

The fact that torque is the product of force 
and moment arm means that if one cannot 
increase force, it is still possible to gain greater 
torque by increasing the moment arm. This is the 
reason why, when one tries and fails to disengage 
a stubborn lug nut, it is a good idea to get a 
longer wrench. Likewise with a lever, greater 
leverage can be gained without applying more 
force: all one needs is a longer lever arm. 

As one might suspect, the lever arm is the 
distance from the force input to the fulcrum, or 
from the fulcrum to the force output. If a car- 
penter is using a nail-puller on the head of a 
hammer to extract a nail from a board, the lever 
arm of force input would be from the carpenter’s 
hand gripping the hammer handle to the place 
where the hammerhead rests against the board. 
The lever arm of force output would be from the 
hammerhead to the end of the nail-puller. 

With a lever, the input force (that of the car- 
penter’s hand pulling back on the hammer han- 
dle) multiplied by the input lever arm is always 
equal to the output force (that of the nail-puller 
pulling up the nail) multiplied by the output 
lever arm. The relationship between input and 
output force and lever arm then makes it possible 
to determine a formula for the lever’s mechanical 
advantage. 

Since F in L in = T out L out (where F = force and L 
= lever arm), it is possible to set up an equation 
for a lever’s mechanical advantage. Once again, 
mechanical advantage is always F lmt /F in , but with 
a lever, it is also L in /L out . Hence, the mechanical 
advantage of a lever is always the same as the 
inverse ratio of the lever arm. If the input arm is 
5 units long and the output arm is 1 unit long, 
the mechanical advantage will be 5, but if the 
positions are reversed, it will be 0.2. 

classes □ f levers. Levers are 
divided into three classes, depending on the rela- 


tive positions of the input lever arm, the fulcrum, 
and the output arm or load. In a Class I lever, 
such as the crowbar and the wrench, the fulcrum 
is between the input arm and the output arm. By 
contrast, a Class II lever, for example, a wheelbar- 
row, places the output force (the load carried in 
the barrow itself) between the input force (the 
action of the operator lifting the handles) and the 
fulcrum, which in this case is the wheel. 

Finally, there is the Class III lever, which is 
the reverse of a Class II. Here, the input force is 
between the output force and the fulcrum. The 
human arm itself is an example of a Class III 
lever: if one grasps a weight in one’s hand, one’s 
bent elbow is the fulcrum, the arm raising the 
weight is the input force, and the weight held in 
the hand — now rising — is the output force. The 
Class III lever has a mechanical advantage of less 
than 1, but what it loses in force output in gains 
in range of motion. 

The world abounds with levers. Among the 
Class I varieties in common use are a nail puller 
on a hammerhead, described earlier, as well as 
postal scales and pliers. A handcart, though it 
might seem at first like a wheelbarrow, is actual- 
ly a Class I lever, because the wheel or fulcrum is 
between the input effort — the force of a person’s 
hands gripping the handles — and the output, 
which is the lifting of the load in the handcart 
itself. Scissors constitute an interesting type of 
Class I lever, because the force of the output (the 
cutting blades) is reduced in order to create a 
greater lever arm for the input, in this case the 
handles gripped when cutting. 

A handheld bottle opener provides an excel- 
lent illustration of a Class II lever. Here the ful- 
crum is on the far end of the opener, away from 
the operator: the top end of the opener ring, 
which rests atop the bottle cap. The cap itself is 
the load, and one provides input force by pulling 
up on the opener handle, thus prying the cap 
from the bottle with the lower end of the opener 
ring. Nail clippers represent a type of combina- 
tion lever: the handle that one operates is a Class 
II, while the cutting blades are a Class III. 

Whereas Class II levers maximize force at the 
expense of range of motion, Class III levers oper- 
ate in exactly the opposite fashion. When using a 
fishing rod to catch a fish, the fisherman’s left 
hand (assuming he is right-handed) constitutes 
the fulcrum as it holds the rod just below the reel 
assembly. The right hand supplies the effort, jerk- 


MECHANICAL 

Advantage 
and Simple 
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SCIENCE □ F EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 6 1 


Mechanical 
Advantage 
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ing upward, while the fish is the load. The pur- 
pose here is not to raise a heavy object (one rea- 
son why a fishing rod may break if one catches 
too large a fish) but rather to use the increased 
lever arm for one’s advantage in catching an 
object at some distance. Similarly, a hammer, 
which constitutes a Class III lever, with the oper- 
ator’s wrist as fulcrum, magnifies the motion of 
the operator’s hand with a hammerhead that cuts 
a much wider arc. 

Many machines that arose in the Industrial 
Age are a combination of many levers — that is, a 
compound lever. In a manual typewriter or 
piano, for instance, each key is a complex assem- 
bly of levers designed for a given task. An auto- 
mobile, too, uses multiple levers — most notably, 
a special variety known as the wheel and axle. 

THE WHEEL AND AXLE. A wheel 

is a variation on a Class I lever, but it represents 
such a stunning technological advancement that 
it deserves to be considered on its own. When 
driving a car, the driver places input force on the 
rim of the steering wheel, whose fulcrum is the 
center of the wheel. The output force is translat- 
ed along the steering column to the driveshaft . 

The combination of wheel and axle over- 
comes one factor that tends to limit the effective- 
ness of most levers, regardless of class: limited 
range of motion. An axle is really a type of wheel, 
though it has a smaller radius, which means that 
the output lever arm is correspondingly smaller. 
Given what was already said about the equation 
for mechanical advantage in a lever, this presents 
a very fortunate circumstance. 

When a wheel turns, it has a relatively large 
lever arm (the rim), that turns a relatively small 
lever arm, the axle. Because the product of input 
force and input lever arm must equal output 
force multiplied by output lever arm, this means 
that the output force will be higher than the 
input force. Therefore, the larger the wheel in 
proportion to the axle, the greater the mechani- 
cal advantage. 

It is for this reason that large vehicles with- 
out power steering often have very large steering 
wheels, which have a larger range of motion and, 
thus, a greater torque on the axle — that is, the 
steering column. Some common examples of the 
wheel-and-axle principle in operation today 
include a doorknob and a screwdriver; however, 
long before the development of the wheel and 
axle, there were wheels alone. 


There is nothing obvious about the wheel, 
and in fact, it is not nearly as old an invention as 
most people think. Until the last few centuries, 
most peoples in sub-Saharan Africa, remote parts 
of central and northern Asia, the Americas, and 
the Pacific Islands remained unaware of it. This 
did not necessarily make them “primitive”: even 
the Egyptians who built the Great Pyramid of 
Cheops in about 2550 B.c. had no concept of the 
wheel. 

What the Egyptians did have, however, were 
rollers — most often logs, onto which a heavy 
object was hoisted using a lever. From rollers 
developed the idea of a sledge, a sled-like device 
for sliding large loads atop a set of rollers. A 
sledge appears in a Sumerian illustration from 
about 3500 b.c., the oldest known representation 
of a wheel-like object. 

The transformation from the roller-and- 
sledge assembly to wheeled vehicles is not as easy 
as it might seem, and historians still disagree as 
to the connection. Whatever the case, it appears 
that the first true wheels originated in Sumer 
(now part of Iraq) in about 3500 b.c. These were 
tripartite wheels, made by attaching three pieces 
of wood and then cutting out a circle. This made 
a much more durable wheel than a sawed-off log, 
and also overcame the fact that few trees are per- 
fectly round. 

During the early period of wheeled trans- 
portation, from 3500 to 2000 b.c., donkeys and 
oxen rather than horses provided the power, in 
part because wheeled vehicles were not yet made 
for the speeds that horses could achieve. Hence, it 
was a watershed event when wheelmakers began 
fashioning axles as machines separate from the 
wheel. Formerly, axles and wheels were made up 
of a single unit; separating them made carts 
much more stable, especially when making 
turns — and, as noted earlier, greatly increased the 
mechanical advantage of the wheels themselves. 

Transportation entered a new phase in about 
2000 B.c., when improvements in technology 
made possible the development of spoked 
wheels. By heat-treating wood, it became possi- 
ble to bend the material slightly, and to attach 
spokes between the rim and hub of the wheel. 
When the wood cooled, the tension created a 
much stronger wheel — capable of carrying heav- 
ier loads faster and over greater distances. 

In China during the first century B.c., a new 
type of wheeled vehicle — identified earlier as a 


| 1 62 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 


Class II lever — was born in the form of the 
wheelbarrow, or “wooden ox.” The wheelbarrow, 
whose invention the Chinese attributed to a 
semi-legendary figure named Ko Yu, was of such 
value to the imperial army for moving arms and 
military equipment that China’s rulers kept its 
design secret for centuries. 

In Europe, around the same time, chariots 
were dying out, and it was a long time before the 
technology of wheeled transport improved. The 
first real innovation came during the 1500s, with 
the development of the horsedrawn coach. By 
1640, a German family was running a regular 
stagecoach service, and, in 1667, a new, light, 
two-wheeled carriage called a cabriolet made its 
first appearance. Later centuries, of course, saw 
the development of increasingly more sophisti- 
cated varieties of wheeled vehicles powered in 
turn by human effort (the bicycle), steam (the 
locomotive), and finally, the internal combustion 
engine (the automobile.) 

But the wheel was never just a machine for 
transport: long before the first wheeled carts 
came into existence, potters had been using 
wheels that rotated in place to fashion perfectly 
round objects, and in later centuries, wheels 
gained many new applications. By 500 b.c., farm- 
ers in Greece and other parts of the Mediter- 
ranean world were using rotary mills powered by 
donkeys. These could grind grain much faster 
than a person working with a hand-powered 
grindstone could hope to do, and in time, the 
Greeks found a means of powering their mills 
with a force more useful than donkeys: water. 

The first waterwheels, turned by human or 
animal power, included a series of buckets along 
the rim that made it possible to raise water from 
the river below and disperse it to other points. By 
about 70 b.c., however, Roman engineers recog- 
nized that they could use the power of water itself 
to turn wheels and grind grain. Thus, the water- 
wheel became one of the first two rotor mecha- 
nisms in which an inanimate source (as opposed 
to the effort of humans or animals) created 
power to spin a shaft. 

In this way, the waterwheel was a prototype 
for the engine developed many centuries later. 
Indeed, in the first century a.d., Hero of Alexan- 
dria — who discovered the concept of steam 
power some 1,700 years before anyone took up 
the idea and put it to use — proposed what has 
been considered a prototype for the turbine 


engine. However, for a variety of complex rea- 
sons, the ancient world was simply not ready for 
the technological leap portended by such an 
invention; and so, in terms of significant progress 
in the development of machines, Europe was 
asleep for more than a millennium. 

The other significant form of wheel powered 
by an “inanimate” source was the windmill, first 
mentioned in 85 b.c. by Antipater of Thessaloni- 
ca, who commented on a windmill he saw in 
northern Greece. In this early version of the 
windmill, the paddle wheel moved on a horizon- 
tal plane. However, the windmill did not take 
hold in Europe during ancient times, and, in fact, 
its true origins lie further east, and it did not 
become widespread until much later. 

In the seventh century a.d., windmills began 
to appear in the region of modern Iran and 
Afghanistan, and the concept spread to the Arab 
world. Europeans in the Near East during the 
Crusades (1095-1291) observed the windmill, 
and brought the idea back to Europe with them. 
By the twelfth century Europeans had developed 
the more familiar vertical mill. 

Finally, there was a special variety of wheel 
that made its appearance as early as 500 b.c.: the 
toothed gearwheel. By 300 b.c., it was in use 
throughout Egypt, and by about 270 b.c., Ctesi- 
bius of Alexandria (fl. c. 270-250 b.c.) had 
applied the gear in devising a constant-flow 
water clock called a clepsydra. 

Some 2,100 years after Ctesibius, toothed 
gears became a critical component of industrial- 
ization. The most common type is a spur gear, in 
which the teeth of the wheel are parallel to the 
axis of rotation. Helical gears, by contrast, have 
curved teeth in a spiral pattern at an angle to 
their rotational axes. This means that several 
teeth of one gearwheel are always in contact with 
several teeth of the adjacent wheel, thus provid- 
ing greater torque. 

In bevel gears, the teeth are straight, as with 
a spur gear, but they slope at a 45°-angle relative 
to their axes so that two gearwheels can fit 
together at up to 90°-angles to one another with- 
out a change in speed. Finally, planetary gears are 
made such that one or more smaller gearwheels 
can fit within a larger gearwheel, which has teeth 
cut on the inside rather than the outside. 

Similar in concept to the gearwheel is the V 
belt drive, which consists of two wheels side by 
side, joined with a belt. Each of the wheels has 


Mechanical 
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and Simple 
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Mechanical 
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grooves cut in it for holding the belt, making this 
a modification of the pulley, and the grooves pro- 
vide much greater gripping power for holding 
the belt in place. One common example of a V 
belt drive, combined with gearwheels, is a bicycle 
chain assembly. 

pulleys. A pulley is essentially a 
grooved wheel on an axle attached to a frame, 
which in turn is attached to some form of rigid 
support such as a ceiling. A rope runs along the 
grooves of the pulley, and one end is attached 
to a load while the other is controlled by the 
operator. 

In several instances, it has been noted that a 
machine may provide increased range of motion 
or position rather than power. So, this simplest 
kind of pulley, known as a single or fixed pulley, 
only offers the advantage of direction rather than 
improved force. When using Venetian blinds, 
there is no increase in force; the advantage of the 
machine is simply that it allows one to move 
objects upward and downward. Thus, the theo- 
retical mechanical advantage of a fixed pulley is 1 
(or almost certainly less under actual conditions, 
where friction is a factor). 

Here it is appropriate to return to 
Archimedes, whose advancements in the under- 
standing of levers translated to improvements in 
pulleys. In the case of the lever, it was Archimedes 
who first recognized that the longer the effort 
arm, the less effort one had to apply in raising the 
load. Likewise, with pulleys and related devices — 
cranes and winches — he explained and improved 
the way these machines worked. 

The first crane device dates to about 1000 
b.c., but evidence from pictures suggests that 
pulleys may have been in use as early as seven 
thousand years before. Several centuries before 
Archimedes’s time, the Greeks were using com- 
pound pulleys that contained several wheels and 
thus provided the operator with much greater 
mechanical advantage than a fixed pulley. 
Archimedes, who was also the first to recognize 
the relationship between pulleys and levers, cre- 
ated the first fully realized block-and-tackle 
system using compound pulleys and cranes. In 
the late modern era, compound pulley systems 
were used in applications such as elevators and 
escalators. 

A compound pulley consists of two or more 
wheels, with at least one attached to the support 
while the other wheel or wheels lift the load. A 


rope runs from the support pulley down to the 
load-bearing wheel, wraps around that pulley 
and comes back up to a fixed attachment on the 
upper pulley. Whereas the upper pulley is fixed, 
the load-bearing pulley is free to move, and rais- 
es the load as the rope is pulled below. 

The simplest kind of compound pulley, with 
just two wheels, has a mechanical advantage of 2. 
On a theoretical level, at least, it is possible to cal- 
culate the mechanical advantage of a compound 
pulley with more wheels: the number is equal to 
the segments of rope between the lower pulleys 
and the upper, or support pulley. In reality, how- 
ever, friction, which is high as ropes rub against 
the pulley wheels, takes its toll. Thus mechanical 
advantage is never as great as it might be. 

A block-and-tackle, like a compound pulley, 
uses just one rope with a number of pulley 
wheels. In a block-and-tackle, however, the 
wheels are arranged along two axles, each of 
which includes multiple pulley wheels that are 
free to rotate along the axle. The upper row is 
attached to the support, and the lower row to the 
load. The rope connects them all, running from 
the first pulley in the upper set to the first in the 
lower set, then to the second in the upper set, and 
so on. In theory, at least, the mechanical advan- 
tage of a block-and-tackle is equal to the number 
of wheels used, which must be an even num- 
ber — but again, friction diminishes the theoreti- 
cal mechanical advantage. 

The Inclined Plane 

To the contemporary mind, it is difficult enough 
to think of a lever as a “machine” — but levers at 
least have more than one part, unlike an inclined 
plane. The latter, by contrast, is exactly what it 
seems to be: a ramp. Yet it was just such a ramp 
structure, as noted earlier, that probably enabled 
the Egyptians to build the pyramids — a feat of 
engineering so stunning that even today, some 
people refuse to believe that the ancient Egyp- 
tians could have achieved it on their own. 

Surely, as anti-scientific proponents of vari- 
ous fantastic theories often insist, the building of 
the pyramids could only have been done with 
machines provided by super-intelligent, extrater- 
restrial beings. Even in ancient times, the Greek 
historian Herodotus (c. 484-c. 424 b.c.) speculat- 
ed that the Egyptians must have used huge cranes 
that had long since disappeared. 


| 1 S4 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


These bizarre guesses concerning the tech- 
nology for raising the pyramid’s giant blocks 
serve to highlight the brilliance of a gloriously 
simple machine that, in essence, doubles force. If 
one needs to move a certain weight to a certain 
height, there are two options. One can either 
raise the weight straight upward, expending an 
enormous amount of effort, even with a pulley 
system; or one can raise the weight gradually 
along an inclined plane. The inclined plane is a 
much wiser choice, because it requires half the 
effort. 

Why half? Imagine an inclined plane sloping 
evenly upward to the right. The plane exists in a 
sort of frame that is equal in both length and 
height to the dimensions of the plane itself. As we 
can easily visualize, the plane takes up exactly 
half of the frame, and this is true whether the 
slope is more than, less than, or equal to 45°. For 
any plane in which the slope is more than 45°, 
however, the mechanical advantage will be less 
than 1, and it is indeed hard to imagine why any- 
one would use such a plane unless forced to do so 
by limitations on their horizontal space — for 
example, when lifting a heavy object from a nar- 
row canyon. 

The mechanical advantage of an inclined 
plane is equal to the ratio between the distance 
over which input force is applied and the dis- 
tance of output; or, more simply, the ratio of 
length to height. If a man is pushing a crate up a 
ramp 4 ft high and 8 ft long (1.22 m by 2.44 m), 
8 ft is the input distance and 4 ft the output dis- 
tance; hence, the mechanical advantage is 2. If the 
ramp length were doubled to 16 ft (4.88 m), the 
mechanical advantage would likewise double to 
4, and so on. 

The concept of work, in terms of physics, has 
specific properties that are a subject unto them- 
selves; however, it is important here only to rec- 
ognize that work is the product of force (that is, 
effort) multiplied by distance. This means that if 
one increases the distance, a much smaller quan- 
tity of force is needed to achieve the same 
amount of work. 

On an everyday level, it is easy to see this in 
action. Walking or running up a gentle hill, obvi- 
ously, is easier than going up a steep hill. There- 
fore, if one’s primary purpose is to conserve 
effort, it is best to choose the gentler hill. On the 
other hand, one may wish to minimize dis- 
tance — or, if moving for the purpose of exercise, 


to maximize force input to burn calories. In 
either case, the steeper hill would be the better 
option. 

wedges. The type of inclined plane 
discussed thus far is a ramp, but there are a num- 
ber of much smaller varieties of inclined plane at 
work in the everyday world. A knife is an excel- 
lent example of one of the most common types, 
a wedge. Again, the mechanical advantage of a 
wedge is the ratio of length to height, which, in 
the knife, would be the depth of the blade com- 
pared to its cross-sectional width. Due to the 
ways in which wedges are used, however, friction 
plays a much greater role, therefore greatly 
reducing the theoretical mechanical advantage. 

Other types of wedges may be used with a 
lever, as a form of fulcrum for raising objects. Or, 
a wedge may be placed under objects to stabilize 
them, as for instance, when a person puts a fold- 
ed matchbook under the leg of a restaurant table 
to stop it from wobbling. Wedges also stop other 
objects from moving: a triangular piece of wood 
under a door will keep it from closing, and a 
more substantial wedge under the front wheels of 
a car will stop it from rolling forward. 

Variations of the wedge are everywhere. 
Consider all the types of cutting or chipping 
devices that exist: scissors, chisels, ice picks, axes, 
splitting wedges (used with a mallet to split a log 
down the center), saws, plows, electric razors, etc. 
Then there are devices that use a complex assem- 
bly of wedges working together. The part of a key 
used to open a lock is really just a row of wedges 
for moving the pins inside the lock to the proper 
position for opening the door. Similarly, each 
tooth in a zipper is a tiny wedge that fits tightly 
with the adjacent teeth. 

screws. As the wheel is, without a 
doubt, the greatest conceptual variation on the 
lever, so the screw may be identified as a particu- 
larly cunning adaptation of an inclined plane. 
The uses of screws today are many and obvious, 
but as with wheels and axles, these machines have 
more applications than are commonly recog- 
nized. Not only are there screws for holding 
things together, but there are screws such as those 
on vises, clamps, or monkey wrenches for apply- 
ing force to objects. 

A screw is an inclined plane in the shape of a 
helix, wrapped around an axis or cylinder. In 
order to determine its mechanical advantage, one 
must first find the pitch, which is the distance 


Mechanical 
Advantage 
and Simple 
Machines 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: real-life physics 


1 65 



A SCREW, LIKE THIS CORKSCREW USED TO OPEN A BOTTLE OF WINE, IS AN INCLINED PLANE IN THE SHAPE OF A 

helix, wrapped around an axis or cylinder. (Ecoscene/Corbis. Reproduced by permission.) 


| 1 66 


between adjacent threads. The other variable is 
lever arm, which with a screwdriver is the radius, 
or on a wrench, the length from the crescent or 
clamp to the area of applied force. Obviously, the 
lever arm is much greater for a wrench, which 
explains why a wrench is sometimes preferable to 
a screwdriver, when removing a highly resistant 
material screw or bolt. 

When one rotates a screw of a given pitch, 
the applied force describes a circle whose area 
may be calculated as 2nL, where L is the lever 
arm. This figure, when divided by the pitch, is the 
same as the ratio between the distance of force 
input to force output. Either number is equal to 
the mechanical advantage for a screw. As suggest- 
ed earlier, that mechanical advantage is usually 
low, because force input (screwing in the screw) 
takes place in a much greater range of motion 
than force output (the screw working its way into 
the surface). But this is exactly what the screw is 
designed to do, and what it lacks in mechanical 
advantage, it more than makes up in its holding 
power. 

As with the lever and pulley, Archimedes did 
not invent the screw, but he did greatly improve 
human understanding of it. Specifically, he 
developed a mathematical formula for a simple 
spiral, and translated this into the highly practi- 

VDLUME 2: REAL-LIFE PHYSICS 


cal Archimedes screw, a device for lifting water. 
The invention consists of a metal pipe in a 
corkscrew shape, which draws water upward as it 
revolves. It proved particularly useful for lifting 
water that had seeped into the lower parts of a 
ship, and in many countries today, it remains in 
use as a simple pump for drawing water out of 
the ground. 

Some historians maintain that Archimedes 
did not invent the screw-type pump, but rather 
saw an example of it in Egypt. In any case, he 
clearly developed a practical version of the 
device, and it soon gained application through- 
out the ancient world. Archaeologists discovered 
a screw-driven olive press in the ruins of Pom- 
peii, destroyed by the eruption of Mt. Vesuvius 
in a.d. 79, and Hero of Alexandria later men- 
tioned the use of a screw-type machine in his 
Mechanica. 

Yet, Archimedes is the figure most widely 
associated with the development of this won- 
drous device. Hence, in 1837, when the Swedish- 
American engineer John Ericsson (1803-1899) 
demonstrated the use of a screw- driven ship’s 
propeller, he did so on a craft he named the 
Archimedes. 

SCIENCE OF EVERYDAY THINGS 




From screws planted in wood to screws that 
drive ships at sea, the device is everywhere in 
modern life. Faucets, corkscrews, drills, and meat 
grinders are obvious examples. Though many 
types of jacks used for lifting an automobile or a 
house are levers, others are screw assemblies on 
which one rotates the handle along a horizontal 
axis. In fact, the jack is a particularly interesting 
device. Versions of the jack represent all three 
types of simple machine: lever, inclined plane, 
and hydraulic press. 

The Hydraulic Press 

As noted earlier, the hydraulic press came into 
existence much, much later than the lever or 
inclined plane, and its birth can be seen within 
the context of a larger movement toward the use 
of water power, including steam. A little more 
than a quarter-century after Pascal created the 
theoretical framework for hydraulic power, his 
countryman Denis Papin (1647-1712) intro- 
duced the steam digester, a prototype for the 
pressure cooker. In 1687, Papin published a work 
describing a machine in which steam operated a 
piston — an early model for the steam engine. 

Papin’s concept, which was on the absolute 
cutting edge of technological development at 
that time, utilized not only steam power but also 
the very hydraulic concept that Pascal had iden- 
tified a few decades earlier. Indeed, the assembly 
of pistons and cylinders that forms the central 
component of the internal-combustion engine 
reflects this hydraulic rule, discovered by Pascal 
in 1653. It was then that he formulated what is 
known as Pascal’s principle: that the external 
pressure applied on a fluid is transmitted 
uniformly throughout the entire body of that 
fluid. 

Inside a piston and cylinder assembly, one of 
the most basic varieties of hydraulic press, the 
pressure is equal to the ratio of force to the hori- 
zontal area of pressure. A simple hydraulic press 
of the variety that might be used to raise a car in 
an auto shop typically consists of two large cylin- 
ders side by side, connected at the bottom by a 
channel in which valves control flow. When one 
applies force over a given area of input — that is, 
by pressing down on one cylinder — this yields a 
uniform pressure that causes output in the sec- 
ond cylinder. 


Once again, mechanical advantage is equal 
to the ratio of force output to force input, and for 
a hydraulic press, this can also be measured as the 
ratio of area output to area input. Just as there is 
an inverse relationship between lever arm and 
force in a lever, and between length and height in 
an inclined plane, so there is such a relationship 
between horizontal area and force in a hydraulic 
pump. Consequently, in order to increase force, 
one should minimize area. 

However, there is another factor to consider: 
height. The mechanical advantage of a hydraulic 
pump is equal to the vertical distance to which 
the input force is applied, divided by that of the 
output force. Hence, the greater the height of the 
input cylinder compared to the output cylinder, 
the greater the mechanical advantage. And since 
these three factors — height, area, and force — 
work together, it is possible to increase the lifting 
force and area by minimizing the height. 

Consider once again the auto-shop car jack. 
Typically, the input cylinder will be relatively tall 
and thin, and the output cylinder short and 
squat. Because the height of the input cylinder is 
large, the area of input will be relatively small, as 
will the force of input. But according to Pascal’s 
principle, whatever the force applied on the 
input, the pressure will be the same on the out- 
put. At the output end, where the car is raised, 
one needs a large amount of force and a relative- 
ly large lifting area. Therefore, height is mini- 
mized to increase force and area. If the output 
area is 10 times the size of the input area, an 
input force of 1 unit will produce an output force 
of 10 units — but in order to raise the weight by 1 
unit of height, the input piston must move 
downward by 10 units. 

This type of car jack provides a basic model 
of the hydraulic press in operation, but, in fact, 
hydraulic technology has many more applica- 
tions. A hydraulic pump, whether for pumping 
air into a tire or water from a basement, uses very 
much the same principle as the hydraulic jack. So 
too does the hydraulic ram, used in machines 
ranging from bulldozers to the hydraulic lifts 
used by firefighters and utility workers to reach 
great heights. 

In a hydraulic ram, however, the characteris- 
tics of the input and output cylinders are 
reversed from those of a car jack. The input 
cylinder, called the master cylinder, is short and 
squat, whereas the output cylinder — the slave 


Mechanical 
Advantage 
and Simple 
Machines 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


1 67 


Mechanical 
Advantage 
and Simple 
Machines 


KEY TERMS 


compound lever: A machine that 

combines multiple levers to accomplish its 
task. An example is a piano or manual 
typewriter. 

class i lever: A lever in which the 

fulcrum is between the input force and 
output force. Examples include a crowbar, 
a nail puller, and scissors. 

class ii lever: A lever in which the 

output force is between the input force and 
the fulcrum. Class II levers, of which 
wheelbarrows and bottle openers are 
examples, maximize output force at the 
expense of range of motion. 

class mi lever: A lever in which 

the input force is between the output force 
and the fulcrum. Class III levers, of which 
a fishing rod is an example, maximize 
range of motion at the expense of output 
force. 

efficiency: The ratio of actual 

mechanical advantage to theoretical 
mechanical advantage. 

f r i cti □ n : The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

fulcrum: The support point of a 

lever. 

inertia: The tendency of an object in 

motion to remain in motion, and of an 
object at rest to remain at rest. 

i n put: The effort supplied by the oper- 

ator of a machine. In a Class I lever such as 


a crowbar, input would be the energy one 
expends by pushing down on the bar. 
Input force is often called applied force, 
effort force, or simply effort. 

lever: One of the three basic varieties 

of machine, a lever consists of a rigid bar 
supported at one point, known as the ful- 
crum. 

lever arm: On a lever, the distance 

from the input force or the output force to 
the fulcrum. 

machine: A device that transmits or 

modifies force or torque for a specific pur- 
pose. 

MECHANICAL ADVANTAGE: The 

ratio of force output to force input for a 
machine. 

moment arm: For an object experi- 

encing torque, moment arm is the distance 
from the pivot or balance point to the vec- 
tor on which force is being applied. 
Moment arm is always perpendicular to 
the direction of force. 

o utput: The results achieved from the 

operation of a machine. In a Class I lever 
such as a crowbar, output is the moving of 
a stone or other heavy load dislodged by 
the crowbar. Output force is often called 
the load or resistance force. 

torque: In general terms, torque is 

turning force; in scientific terms, it is 
the product of moment arm multiplied 
by force. 


cylinder — is tall and thin. The reason for this 
change is that in objects using a hydraulic ram, 
height is more important than force output: they 


are often raising people rather than cars. When 
the slave cylinder exerts pressure on the stabilizer 
ram above it (the bucket containing the firefight- 


| 1 SB 


VOLUME 2: real-life physics 


SCIENCE OF EVERYDAY THINGS 



er, for example), it rises through a much larger 
range of vertical motion than that of the fluid 
flowing from the master cylinder. 

As noted earlier, the pistons of a car engine 
are hydraulic pumps — specifically, reciprocating 
hydraulic pumps, so named because they all 
work together. In scientific terms, “fluid” can 
mean either a liquid or a gas such as air; hence, 
there is an entire subset of hydraulic machines 
that are pneumatic, or air-powered. Among these 
are power brakes in a car, pneumatic drills, and 
even hovercrafts. As with the other two varieties 
of simple machine, the hydraulic press is in evi- 
dence throughout virtually every nook and cran- 
ny of daily life. The pump in a toilet tank is a type 
of hydraulic press, as is the inner chamber of a 
pen. So too are aerosol cans, fire extinguishers, 
scuba tanks, water meters, and pressure gauges. 

WHERE TD LEARN MORE 

Archimedes (Web site), <http://www.mcs.drexel.edu/ 
~crorres/Archimedes/contents.html> (March 9, 
2001.) 


Bains, Rae. Simple Machines. Mahwah, N.J.: Troll Associ- 
ates, 1985. 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Canizares, Susan. Simple Machines. New York: Scholastic, 
1999. 

Haslam, Andrew and David Glover. Machines. Photogra- 
phy by Jon Barnes. Chicago: World Book, 1998. 

“Inventors Toolbox: The Elements of Machines” (Web 
site). <http://www.mos.org/sln/Leonardo/Inven- 
torsToolbox.html> (March 9, 2001). 

Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

“Machines” (Web site). <http://www.galaxy.net:80/~kl2/ 
machines/index.s.html> (March 9, 2001). 

“Motion, Energy, and Simple Machines” (Web site). 
<http://www.necc.mass.edu/MRVIS/MR3_13/start. 
html> (March 9, 2001). 

O’Brien, Robert, and the Editors of Life. Machines. New 
York: Time-Life Books, 1964. 

“Simple Machines” (Web site), <http://sln.fi.edu/qa97/ 
spotlight3/spotlight3.html> (March 9, 2001). 

Singer, Charles Joseph, et al., editors. A History of Tech- 
nology (8 vols.) Oxford, England: Clarendon Press, 
1954-84. 


Mechanical 
Advantage 
and Simple 
Machines 


1 69 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


ENERGY 


C □ N C E PT 

As with many concepts in physics, energy — along 
with the related ideas of work and power — has a 
meaning much more specific, and in some ways 
quite different, from its everyday connotation. 
According to the language of physics, a person 
who strains without success to pull a rock out of 
the ground has done no work, whereas a child 
playing on a playground produces a great deal of 
work. Energy, which may be defined as the abili- 
ty of an object to do work, is neither created nor 
destroyed; it simply changes form, a concept 
that can be illustrated by the behavior of a 
bouncing ball. 

H □ W IT WDRKS 

In fact, it might actually be more precise to say 
that energy is the ability of “a thing” or “some- 
thing” to do work. Not only tangible objects 
(whether they be organic, mechanical, or electro- 
magnetic) but also non-objects may possess 
energy. At the subatomic level, a particle with no 
mass may have energy. The same can be said of a 
magnetic force field. 

One cannot touch a force field; hence, it is 
not an object — but obviously, it exists. All one 
has to do to prove its existence is to place a natu- 
ral magnet, such as an iron nail, within the mag- 
netic field. Assuming the force field is strong 
enough, the nail will move through space toward 
it — and thus the force field will have performed 
work on the nail. 

Wdrk: What It Is and Is Not 

Work may be defined in general terms as the 
exertion of force over a given distance. In order 

VDLUME 2: REAL-LIFE PHYSICS 


for work to be accomplished, there must be a dis- 
placement in space — or, in colloquial terms, 
something has to be moved from point A to 
point B. As noted earlier, this definition creates 
results that go against the common-sense defini- 
tion of “work.” 

A person straining, and failing, to pull a rock 
from the ground has performed no work (in 
terms of physics) because nothing has been 
moved. On the other hand, a child on a play- 
ground performs considerable work: as she runs 
from the slide to the swing, for instance, she has 
moved her own weight (a variety of force) across 
a distance. She is even working when her move- 
ment is back-and-forth, as on the swing. This 
type of movement results in no net displacement, 
but as long as displacement has occurred at all, 
work has occurred. 

Similarly, when a man completes a full push- 
up, his body is in the same position — parallel to 
the floor, arms extended to support him — as he 
was before he began it; yet he has accomplished 
work. If, on the other hand, he at the end of his 
energy, his chest is on the floor, straining but fail- 
ing, to complete just one more push-up, then he 
is not working. The fact that he feels as though he 
has worked may matter in a personal sense, but it 
does not in terms of physics. 

calculating wdrk. Work can 
be defined more specifically as the product of 
force and distance, where those two vectors are 
exerted in the same direction. Suppose one were 
to drag a block of a certain weight across a given 
distance of floor. The amount of force one exerts 
parallel to the floor itself, multiplied by the dis- 
tance, is equal to the amount of work exerted. On 
the other hand, if one pulls up on the block in a 

science df everyday things 




While this player dribbles his basketball, the ball experiences a complex energy transfer as it hits 
the flo □ r and BOUNCES back up. (Photograph by David Katzenstein/Corbis. Reproduced by permission.) 


position perpendicular to the floor, that force 
does not contribute toward the work of dragging 
the block across the floor, because it is not par 
allel to distance as defined in this particular 
situation. 

Similarly, if one exerts force on the block at 
an angle to the floor, only a portion of that force 
counts toward the net product of work — a por- 
tion that must be quantified in terms of 
trigonometry. The line of force parallel to the 
floor may be thought of as the base of a triangle, 
with a line perpendicular to the floor as its sec- 
ond side. Hence there is a 90°-angle, making it a 
right triangle with a hypotenuse. The hypotenuse 
is the line of force, which again is at an angle to 
the floor. 

The component of force that counts toward 
the total work on the block is equal to the total 
force multiplied by the cosine of the angle. A 
cosine is the ratio between the leg adjacent to an 
acute (less than 90°) angle and the hypotenuse. 
The leg adjacent to the acute angle is, of course, 
the base of the triangle, which is parallel to the 
floor itself. Sizes of triangles may vary, but the 
ratio expressed by a cosine (abbreviated cos) 
does not. Hence, if one is pulling on the block by 
a rope that makes a 30°-angle to the floor, then 

SCIENCE □ E EVERYDAY THINGS 


force must be multiplied by cos 30°, which is 
equal to 0.866. 

Note that the cosine is less than 1; hence 
when multiplied by the total force exerted, it will 
yield a figure 13.4% smaller than the total force. 
In fact, the larger the angle, the smaller the 
cosine; thus for 90°, the value of cos = 0. On the 
other hand, for an angle of 0°, cos = 1. Thus, if 
total force is exerted parallel to the floor — that is, 
at a 0°-angle to it — then the component of force 
that counts toward total work is equal to the total 
force. From the standpoint of physics, this would 
be a highly work-intensive operation. 

GRAVITY AND CITHER PECU- 
LIARITIES of work. The above dis- 
cussion relates entirely to work along a horizon- 
tal plane. On the vertical plane, by contrast, work 
is much simpler to calculate due to the presence 
of a constant downward force, which is, of 
course, gravity. The force of gravity accelerates 
objects at a rate of 32 ft (9.8 m)/sec 2 . The mass 
(m) of an object multiplied by the rate of gravi- 
tational acceleration (g) yields its weight, and the 
formula for work done against gravity is equal to 
weight multiplied by height ( h ) above some 
lower reference point: mgh. 

VDLUME 2: REAL-LIFE PHYSICS 


1 V 1 


Energy 



Hydroelectric dams, like the Shasta dam in California, superbly illustrate the principle of energy 
conversion. (Photograph by Charles E. Rotkin/Corbis. Reproduced by permission.) 


| 1 72 


Distance and force are both vectors — that is, 
quantities possessing both magnitude and direc- 
tion. Yet work, though it is the product of these 
two vectors, is a scalar, meaning that only the 
magnitude of work (and not the direction over 
which it is exerted) is important. Hence mgh can 
refer either to the upward work one exerts 
against gravity (that is, by lifting an object to a 
certain height), or to the downward work that 
gravity performs on the object when it is 
dropped. The direction of h does not matter, and 
its value is purely relative, referring to the vertical 
distance between one point and another. 

The fact that gravity can “do work” — and 
the irrelevance of direction — further illustrates 

VDLUME 2: REAL-LIFE PHYSICS 


the truth that work, in the sense in which it is 
applied by physicists, is quite different from 
“work” as it understood in the day-to-day world. 
There is a highly personal quality to the everyday 
meaning of the term, which is completely lacking 
from its physics definition. 

If someone carried a heavy box up five 
flights of stairs, that person would quite natural- 
ly feel justified in saying “I’ve worked.” Certainly 
he or she would feel that the work expended was 
far greater than that of someone who had simply 
allowed the the elevator to carry the box up those 
five floors. Yet in terms of work done against 
gravity, the work done on the box by the elevator 
is exactly the same as that performed by the per- 

SCIENCE OF EVERYDAY THINGS 




son carrying it upstairs. The identity of the 
“worker” — not to mention the sweat expended 
or not expended — is irrelevant from the stand- 
point of physics. 

Measurement of Work and 
Pdwer 

In the metric system, a newton (N) is the amount 
of force required to accelerate 1 kg of mass by 1 
meter per second squared (m/s 2 ). Work is meas- 
ured by the joule ( J), equal to 1 newton-meter (N 
• m). The British unit of force is the pound, and 
work is measured in foot-pounds, or the work 
done by a force of 1 lb over a distance of one foot. 

Power, the rate at which work is accom- 
plished over time, is the same as work divided by 
time. It can also be calculated in terms of force 
multiplied by speed, much like the force-multi- 
plied-by-distance formula for work. However, as 
with work, the force and speed must be in the 
same direction. Hence, the formula for power in 
these terms is F • cos 0 • v, where F=force, 
v=speed, and cos 0 is equal to the cosine of the 
angle 0 (the Greek letter theta) between F and the 
direction of v. 

The metric-system measure of power is the 
watt, named after James Watt (1736-1819), the 
Scottish inventor who developed the first fully 
viable steam engine and thus helped inaugurate 
the Industrial Revolution. A watt is equal to 1 
joule per second, but this is such a small unit that 
it is more typical to speak in terms of kilowatts, 
or units of 1,000 watts. 

Ironically, Watt himself — like most people in 
the British Isles and America — lived in a world 
that used the British system, in which the unit of 
power is the foot-pound per second. The latter, 
too, is very small, so for measuring the power of 
his steam engine, Watt suggested a unit based on 
something quite familiar to the people of his 
time: the power of a horse. One horsepower (hp) 
is equal to 550 foot-pounds per second. 

SDRTING OUT METRIC AND 

British units. The British system, of 
course, is horridly cumbersome compared to the 
metric system, and thus it long ago fell out of 
favor with the international scientific communi- 
ty. The British system is the product of loosely 
developed conventions that emerged over time: 
for instance, a foot was based on the length of the 
reigning king’s foot, and in time, this became 
standardized. By contrast, the metric system was 

SCIENCE DF EVERYDAY THINES 



In this 195V photograph, Italian opera singer 
Luigi Infantino tries to break a wine glass by 

SINGING A HIGH “C” NOTE. CONTRARY TO POPULAR 
BELIEF, THE NOTE DOES NOT HAVE TO BE A PARTICU- 
LARLY HIGH ONE TO BREAK THE GLASS: RATHER, THE 
NOTE SHOULD BE ON THE SAME WAVELENGTH AS THE 

glass’s own vibrations. When this occurs, 

SOUND ENERGY IS TRANSFERRED DIRECTLY TO THE 
GLASS, WHICH IS SHATTERED BY THIS SUDDEN NET 

intake of energy. (Hulton-Deutsch Collection/ Corbis. Repro- 
duced by permission.) 

created quite deliberately over a matter of just a 
few years following the French Revolution, which 
broke out in 1789. The metric system was adopt- 
ed ten years later. 

During the revolutionary era, French intel- 
lectuals believed that every aspect of existence 
could and should be treated in highly rational, 
scientific terms. Out of these ideas arose much 
folly — especially after the supposedly “rational” 
leaders of the revolution began chopping off 
people’s heads — but one of the more positive 
outcomes was the metric system. This system, 
based entirely on the number 10 and its expo- 
nents, made it easy to relate one figure to anoth- 
er: for instance, there are 100 centimeters in a 
meter and 1,000 meters in a kilometer. This is 
vastly more convenient than converting 12 inch- 
es to a foot, and 5,280 feet to a mile. 

VDLUME 2: REAL-LIFE PHYSIGS 


Energy 


1 73 



Energy 


| 1 74 


For this reason, scientists — even those from 
the Anglo-American world — use the metric sys- 
tem for measuring not only horizontal space, but 
volume, temperature, pressure, work, power, and 
so on. Within the scientific community, in fact, 
the metric system is known as SI, an abbreviation 
of the French Systeme International d’Unites — 
that is, “International System of Units.” 

Americans have shown little interest in 
adopting the SI system, yet where power is con- 
cerned, there is one exception. For measuring the 
power of a mechanical device, such as an auto- 
mobile or even a garbage disposal, Americans use 
the British horsepower. However, for measuring 
electrical power, the SI kilowatt is used. When an 
electric utility performs a meter reading on a 
family’s power usage, it measures that usage in 
terms of electrical “work” performed for the fam- 
ily, and thus bills them by the kilowatt-hour. 

Three Types df Energy 

KINETIC AND POTENTIAL EN- 
ERGY formulae. Earlier, energy was 
defined as the ability of an object to accomplish 
work — a definition that by this point has 
acquired a great deal more meaning. There are 
three types of energy: kinetic energy, or the ener- 
gy that something possesses by virtue of its 
motion; potential energy, the energy it possesses 
by virtue of its position; and rest energy, the 
energy it possesses by virtue of its mass. 

The formula for kinetic energy is KE = 'A 
mv 2 . In other words, for an object of mass m, 
kinetic energy is equal to half the mass multi- 
plied by the square of its speed v. The actual der- 
ivation of this formula is a rather detailed 
process, involving reference to the second of the 
three laws of motion formulated by Sir Isaac 
Newton (1642-1727.) The second law states that 
F = ma, in other words, that force is equal to mass 
multiplied by acceleration. In order to under- 
stand kinetic energy, it is necessary, then, to 
understand the formula for uniform accelera- 
tion. The latter is v? = v 0 2 + las, where v? is the 
final speed of the object, v 0 2 its initial speed, a 
acceleration and s distance. By substituting val- 
ues within these equations, one arrives at the for- 
mula of / mv 2 for kinetic energy. 

The above is simply another form of the 
general formula for work — since energy is, after 
all, the ability to perform work. In order to pro- 
duce an amount of kinetic energy equal to 'A mv 2 

VDLUME 2: REAL-LIFE PHYSICS 


within an object, one must perform an amount 
of work on it equal to Fs. Hence, kinetic energy 
also equals Fs, and thus the preceding paragraph 
simply provides a means for translating that into 
more specific terms. 

The potential energy (PE) formula is much 
simpler, but it also relates to a work formula 
given earlier: that of work done against gravity. 
Potential energy, in this instance, is simply a 
function of gravity and the distance h above 
some reference point. Hence, its formula is the 
same as that for work done against gravity, mgh 
or wh, where w stands for weight. (Note that this 
refers to potential energy in a gravitational field; 
potential energy may also exist in an electromag- 
netic field, in which case the formula would be 
different from the one presented here.) 

REST ENERGY AND ITS IN- 
TRIGUING formula. Finally, there is 
rest energy, which, though it may not sound very 
exciting, is in fact the most intriguing — and the 
most complex — of the three. Ironically, the for- 
mula for rest energy is far, far more complex in 
derivation than that for potential or even kinetic 
energy, yet it is much more well-known within 
the popular culture. 

Indeed, E = me 2 is perhaps the most famous 
physics formula in the world — even more so 
than the much simpler F = ma. The formula for 
rest energy, as many people know, comes from 
the man whose Theory of Relativity invalidated 
certain specifics of the Newtonian framework: 
Albert Einstein (1879-1955). As for what the for- 
mula actually means, that will be discussed later. 

REAL-LIFE 
A P P L I C AT I □ N S 

Falling and Bouncing Balls 

One of the best — and most frequently used — 
illustrations of potential and kinetic energy 
involves standing at the top of a building, hold- 
ing a baseball over the side. Naturally, this is not 
an experiment to perform in real life. Due to its 
relatively small mass, a falling baseball does not 
have a great amount of kinetic energy, yet in the 
real world, a variety of other conditions (among 
them inertia, the tendency of an object to main- 
tain its state of motion) conspire to make a hit on 
the head with a baseball potentially quite serious. 

SCIENCE DF EVERYDAY THINGS 


Energy 


If dropped from a great enough height, it could 
be fatal. 

When one holds the baseball over the side of 
the building, potential energy is at a peak, but 
once the ball is released, potential energy begins 
to decrease in favor of kinetic energy. The rela- 
tionship between these, in fact, is inverse: as the 
value of one decreases, that of the other increas- 
es in exact proportion. The ball will only fall to 
the point where its potential energy becomes 0, 
the same amount of kinetic energy it possessed 
before it was dropped. At the same point, kinetic 
energy will have reached maximum value, and 
will be equal to the potential energy the ball pos- 
sessed at the beginning. Thus the sum of kinetic 
energy and potential energy remains constant, 
reflecting the conservation of energy, a subject 
discussed below. 

It is relatively easy to understand how the 
ball acquires kinetic energy in its fall, but poten- 
tial energy is somewhat more challenging to 
comprehend. The ball does not really “possess” 
the potential energy: potential energy resides 
within an entire system comprised by the ball, 
the space through which it falls, and the Earth. 
There is thus no “magic” in the reciprocal rela- 
tionship between potential and kinetic energy: 
both are part of a single system, which can be 
envisioned by means of an analogy. 

Imagine that one has a 20-dollar bill, then 
buys a pack of gum. Now one has, say, $19.20. 
The positive value of dollars has decreased by 
$0.80, but now one has increased “non-dollars” 
or “anti-dollars” by the same amount. After buy- 
ing lunch, one might be down to $12.00, mean- 
ing that “anti-dollars” are now up to $8.00. The 
same will continue until the entire $20.00 has 
been spent. Obviously, there is nothing magical 
about this: the 20-dollar bill was a closed system, 
just like the one that included the ball and the 
ground. And just as potential energy decreased 
while kinetic energy increased, so “non-dollars” 
increased while dollars decreased. 

bouncing back. The example of 
the baseball illustrates one of the most funda- 
mental laws in the universe, the conservation of 
energy: within a system isolated from all other 
outside factors, the total amount of energy 
remains the same, though transformations of 
energy from one form to another take place. An 
interesting example of this comes from the case 

SCIENCE OF EVERYDAY THINGS 


of another ball and another form of vertical 
motion. 

This time instead of a baseball, the ball 
should be one that bounces: any ball will do, 
from a basketball to a tennis ball to a superball. 
And rather than falling from a great height, this 
one is dropped through a range of motion ordi- 
nary for a human being bouncing a ball. It hits 
the floor and bounces back — during which time 
it experiences a complex energy transfer. 

As was the case with the baseball dropped 
from the building, the ball (or more specifically, 
the system involving the ball and the floor) pos- 
sesses maximum potential energy prior to being 
released. Then, in the split-second before its 
impact on the floor, kinetic energy will be at a 
maximum while potential energy reaches zero. 

So far, this is no different than the baseball 
scenario discussed earlier. But note what happens 
when the ball actually hits the floor: it stops for 
an infinitesimal fraction of a moment. What has 
happened is that the impact on the floor (which 
in this example is assumed to be perfectly rigid) 
has dented the surface of the ball, and this saps 
the ball’s kinetic energy just at the moment when 
the energy had reached its maximum value. In 
accordance with the energy conservation law, 
that energy did not simply disappear: rather, it 
was transferred to the floor. 

Meanwhile, in the wake of its huge energy 
loss, the ball is motionless. An instant later, how- 
ever, it reabsorbs kinetic energy from the floor, 
undents, and rebounds. As it flies upward, its 
kinetic energy begins to diminish, but potential 
energy increases with height. Assuming that the 
person who released it catches it at exactly the 
same height at which he or she let it go, then 
potential energy is at the level it was before the 
ball was dropped. 

WHEN A BALL LOSES ITS 

bounce. The above, of course, takes little 
account of energy “loss” — that is, the transfer of 
energy from one body to another. In fact, a part 
of the ball’s kinetic energy will be lost to the floor 
because friction with the floor will lead to an 
energy transfer in the form of thermal, or heat, 
energy. The sound that the ball makes when it 
bounces also requires a slight energy loss; but 
friction — a force that resists motion when the 
surface of one object comes into contact with the 
surface of another — is the principal culprit 
where energy transfer is concerned. 

VDLUME 2: REAL-LIFE PHYSICS 


1 75 


Energy 


1 76 


Of particular importance is the way the ball 
responds in that instant when it hits bottom and 
stops. Hard rubber balls are better suited for this 
purpose than soft ones, because the harder the 
rubber, the greater the tendency of the molecules 
to experience only elastic deformation. What this 
means is that the spacing between molecules 
changes, yet their overall position does not. 

If, however, the molecules change positions, 
this causes them to slide against one another, 
which produces friction and reduces the energy 
that goes into the bounce. Once the internal fric- 
tion reaches a certain threshold, the ball is 
“dead” — that is, unable to bounce. The deader 
the ball is, the more its kinetic energy turns into 
heat upon impact with the floor, and the less 
energy remains for bouncing upward. 

Varieties of Energy in Actiein 

The preceding illustration makes several refer- 
ences to the conversion of kinetic energy to ther- 
mal energy, but it should be stressed that there 
are only three fundamental varieties of energy: 
potential, kinetic, and rest. Though heat is often 
discussed as a form unto itself, this is done only 
because the topic of heat or thermal energy is 
complex: in fact, thermal energy is simply a result 
of the kinetic energy between molecules. 

To draw a parallel, most languages permit 
the use of only three basic subject-predicate con- 
structions: first person (“I”), second person 
(“you”), and third person (“he/she/it”) Yet with- 
in these are endless varieties such as singular and 
plural nouns or various temporal orientations of 
verbs: present (“I go”); present perfect (“I have 
gone”); simple past (“I went”); past perfect (“I 
had gone.”) There are even “moods,” such as the 
subjunctive or hypothetical, which permit the 
construction of complex thoughts such as “I 
would have gone.” Yet for all this variety in terms 
of sentence pattern — actually, a degree of variety 
much greater than for that of energy types — all 
subject-predicate constructions can still be iden- 
tified as first, second, or third person. 

One might thus describe thermal energy as a 
manifestation of energy, rather than as a discrete 
form. Other such manifestations include electro- 
magnetic (sometimes divided into electrical and 
magnetic), sound, chemical, and nuclear. The 
principles governing most of these are similar: 
for instance, the positive or negative attraction 

VDLUME 2: REAL-LIFE PHYSICS 


between two electromagnetically charged parti- 
cles is analogous to the force of gravity. 

mechanical energy. One term 
not listed among manifestations of energy is 
mechanical energy, which is something different 
altogether: the sum of potential and kinetic ener- 
gy. A dropped or bouncing ball was used as a 
convenient illustration of interactions within a 
larger system of mechanical energy, but the 
example could just as easily have been a roller 
coaster, which, with its ups and downs, quite 
neatly illustrates the sliding scale of kinetic and 
potential energy. 

Likewise, the relationship of Earth to the 
Sun is one of potential and kinetic energy trans- 
fers: as with the baseball and Earth itself, the 
planet is pulled by gravitational force toward the 
larger body. When it is relatively far from the 
Sun, it possesses a higher degree of potential 
energy, whereas when closer, its kinetic energy is 
highest. Potential and kinetic energy can also be 
illustrated within the realm of electromagnetic, 
as opposed to gravitational, force: when a nail is 
some distance from a magnet, its potential ener- 
gy is high, but as it moves toward the magnet, 
kinetic energy increases. 

ENERGY conversion in a 
dam. A dam provides a beautiful illustration 
of energy conversion: not only from potential to 
kinetic, but from energy in which gravity pro- 
vides the force component to energy based in 
electromagnetic force. A dam big enough to be 
used for generating hydroelectric power forms a 
vast steel-and-concrete curtain that holds back 
millions of tons of water from a river or other 
body. The water nearest the top — the “head” of 
the dam — thus has enormous potential energy. 

Hydroelectric power is created by allowing 
controlled streams of this water to flow down- 
ward, gathering kinetic energy that is then trans- 
ferred to powering turbines. Dams in popular 
vacation spots often release a certain amount of 
water for recreational purposes during the day. 
This makes it possible for rafters, kayakers, and 
others downstream to enjoy a relatively fast- flow- 
ing river. (Or, to put it another way, a stream with 
high kinetic energy.) As the day goes on, howev- 
er, the sluice-gates are closed once again to build 
up the “head.” Thus when night comes, and ener- 
gy demand is relatively high as people retreat to 
their homes, vacation cabins, and hotels, the dam 
is ready to provide the power they need. 

SCIENCE DF EVERYDAY THINGS 


OTHER MANIFESTATIONS OF 

energy. Thermal and electromagnetic 
energy are much more readily recognizable man- 
ifestations of energy, yet sound and chemical 
energy are two forms that play a significant part 
as well. Sound, which is essentially nothing more 
than the series of pressure fluctuations within a 
medium such as air, possesses enormous energy: 
consider the example of a singer hitting a certain 
note and shattering a glass. 

Contrary to popular belief, the note does not 
have to be particularly high: rather, the note 
should be on the same wavelength as the glass’s 
own vibrations. When this occurs, sound energy 
is transferred directly to the glass, which is shat- 
tered by this sudden net intake of energy. Sound 
waves can be much more destructive than that: 
not only can the sound of very loud music cause 
permanent damage to the ear drums, but also, 
sound waves of certain frequencies and decibel 
levels can actually drill through steel. Indeed, 
sound is not just a by-product of an explosion; it 
is part of the destructive force. 

As for chemical energy, it is associated with 
the pull that binds together atoms within larger 
molecular structures. The formation of water 
molecules, for instance, depends on the chemical 
bond between hydrogen and oxygen atoms. The 
combustion of materials is another example of 
chemical energy in action. 

With both chemical and sound energy, how- 
ever, it is easy to show how these simply reflect 
the larger structure of potential and kinetic ener- 
gy discussed earlier. Hence sound, for instance, is 
potential energy when it emerges from a source, 
and becomes kinetic energy as it moves toward a 
receiver (for example, a human ear). Further- 
more, the molecules in a combustible material 
contain enormous chemical potential energy, 
which becomes kinetic energy when released 
in a fire. 

Rest Energy and Its Nuclear 
Manifestation 

Nuclear energy is similar to chemical energy, 
though in this instance, it is based on the binding 
of particles within an atom and its nucleus. But it 
is also different from all other kinds of energy, 
because its force component is neither gravita- 
tional nor electromagnetic, but based on one of 
two other known varieties of force: strong 
nuclear and weak nuclear. Furthermore, nuclear 

science of everyday things 


energy — to a much greater extent than thermal 
or chemical energy — involves not only kinetic 
and potential energy, but also the mysterious, 
extraordinarily powerful, form known as rest 
energy. 

Throughout this discussion, there has been 
little mention of rest energy; yet it is ever-pres- 
ent. Kinetic and potential energy rise and fall 
with respect to one another; but rest energy 
changes little. In the baseball illustration, for 
instance, the ball had the same rest energy at the 
top of the building as it did in flight — the same 
rest energy, in fact, that it had when sitting on the 
ground. And its rest energy is enormous. 

nuclear warfare. This brings 
back the subject of the rest energy formula: E = 
me 1 , famous because it made possible the cre- 
ation of the atomic bomb. The latter, which for- 
tunately has been detonated in warfare only twice 
in history, brought a swiff end to World War II 
when the United States unleashed it against 
Japan in August 1945. From the beginning, it was 
clear that the atom bomb possessed staggering 
power, and that it would forever change the way 
nations conducted their affairs in war and peace. 

Yet the atom bomb involved only nuclear fis- 
sion, or the splitting of an atom, whereas the 
hydrogen bomb that appeared just a few years 
after the end of World War II used an even more 
powerful process, the nuclear fusion of atoms. 
Hence, the hydrogen bomb upped the ante to a 
much greater extent, and soon the two nuclear 
superpowers — the United States and the Soviet 
Union — possessed the power to destroy most of 
the life on Earth. 

The next four decades were marked by a 
superpower struggle to control “the bomb” as it 
came to be known — meaning any and all nuclear 
weapons. Initially, the United States controlled all 
atomic secrets through its heavily guarded Man- 
hattan Project, which created the bombs used 
against Japan. Soon, however, spies such as Julius 
and Ethel Rosenberg provided the Soviets with 
U.S. nuclear secrets, ensuring that the dictator- 
ship of Josef Stalin would possess nuclear capa- 
bilities as well. (The Rosenbergs were executed 
for treason, and their alleged innocence became a 
celebrated cause among artists and intellectuals; 
however, Soviet documents released since the 
collapse of the Soviet empire make it clear that 
they were guilty as charged.) 

VDLUME 2: REAL-LIFE PHYSICS 


Energy 


1 77 


Energy 


KEY TERMS 


C □ N 5 E RVATI □ N DF ENERGY: A 

law of physics which holds that within a 
system isolated from all other outside fac- 
tors, the total amount of energy re-mains 
the same, though transformations of ener- 
gy from one form to another take place. 

cgsine: For an acute (less than 90°) 

in a right triangle, the cosine (abbreviated 
cos) is the ratio between the adjacent leg 
and the hypotenuse. Regardless of the size 
of the triangle, this figure is a constant for 
any particular angle. 

energy: The ability of an object (or 

in some cases a non-object, such as a mag- 
netic force field) to accomplish work. 

friction: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

horsepower: The British unit of 

power, equal to 550 foot-pounds per 
second. 

hypotenuse: In a right triangle, the 

side opposite the right angle. 


joule: The SI measure of work. One 

joule (1 J) is equal to the work required 
to accelerate 1 kilogram of mass by 1 
meter per second squared (1 m/s 2 ) over a 
distance of 1 meter. Due to the small size 
of the joule, however, it is often replaced 
by the kilowatt-hour, equal to 3.6 million 
(3.6 • 106) J. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 

matter: Physical substance that occu- 

pies space, has mass, is composed of atoms 
(or in the case of subatomic particles, is 
part of an atom), and is convertible into 
energy. 

MECHANICAL ENERGY: The Sum of 

potential energy and kinetic energy within 
a system. 

potential energy: The energy 

that an object possesses by virtue of its 
position. 

pdwer: The rate at which work is 

accomplished over time, a figure rendered 
mathematically as work divided by time. 


| 1 78 


Both nations began building up missile arse- 
nals. It was not, however, just a matter of the 
United States and the Soviet Union. By the 1970s, 
there were at least three other nations in the 
“nuclear club”: Britain, France, and China. There 
were also other countries on the verge of devel- 
oping nuclear bombs, among them India and 
Israel. Furthermore, there was a great threat that 
a terrorist leader such as Libya’s Muammar al- 
Qaddafi would acquire nuclear weapons and do 
the unthinkable: actually use them. 

Though other nations acquired nuclear 
weapons, however, the scale of the two super- 
power arsenals dwarfed all others. And at the 
heart of the U.S. -Soviet nuclear competition was 

VDLUME z: real-life physics 


a sort of high-stakes chess game — to use a 
metaphor mentioned frequently during the 
1970s. Soviet leaders and their American coun- 
terparts both recognized that it would be the end 
of the world if either unleashed their nuclear 
weapons; yet each was determined to be able to 
meet the other’s ever-escalating nuclear threat. 

United States President Ronald Reagan 
earned harsh criticism at home for his nuclear 
buildup and his hard line in negotiations with 
Soviet President Mikhail Gorbachev; but as a 
result of this one-upmanship, he put the Soviets 
into a position where they could no longer com- 
pete. As they put more and more money into 
nuclear weapons, they found themselves less and 

SCIENCE of everyday things 



Energy 


KEY TERMS continued 


The SI unit of power is the watt, while the 
British unit is the foot-pound per second. 
The latter, because it is small, is usually 
reckoned in terms of horsepower. 

rest energy: The energy an object 

possesses by virtue of its mass. 

right triangle: A triangle that 

includes a right (90°) angle. The other two 
angles are, by definition, acute or less 
than 90°. 

scalar: A quantity that possesses 

only magnitude, with no specific direction. 

si: An abbreviation of the French 

Systeme International d’Unites, which 
means “International System of Units.” 
This is the term within the scientific com- 
munity for the entire metric system, as 
applied to a wide variety of quantities 
ranging from length, weight and volume to 
work and power, as well as electromag- 
netic units. 

system: In discussions of energy, the 

term “system” refers to a closed set of inter- 


actions free from interference by outside 
factors. An example is the baseball dropped 
from a height to illustrate potential energy 
and kinetic energy the ball, the space 
through which it falls, and the ground 
below together form a system. 

vector: A quantity that possesses 

both magnitude and direction. 

watt: The metric unit of power, equal 

to 1 joule per second. Because this is such a 
small unit, scientists and engineers typical- 
ly speak in terms of kilowatts, or units of 
1,000 watts. 

work: The exertion of force over a 

given distance. Work is the product of force 
and distance, where force and distance are 
exerted in the same direction. Hence the 
actual formula for work is F • cos 0 • s, 
where F = force, s = distance, and cos 0 is 
equal to the cosine of the angle 0 (the 
Greek letter theta) between F and s. In the 
metric or SI system, work is measured by 
the joule (J), and in the British system by 
the foot-pound. 


less able to uphold their already weak economic 
system. This was precisely Reagan’s purpose in 
using American economic might to outspend the 
Soviets — or, in the case of the proposed multi- 
trillion-dollar Strategic Defense Initiative (SDI 
or “Star Wars”) — threatening to outspend them. 
The Soviets expended much of their economic 
energy in competing with U.S. military strength, 
and this (along with a number of other complex 
factors), spelled the beginning of the end of the 
Communist empire. 

e = m c 2 . The purpose of the preceding 
historical brief is to illustrate the epoch-making 
significance of a single scientific formula: E = 
me 2 . It ended World War II and ensured that no 

SCIENCE DF EVERYDAY THINGS 


war like it would ever happen again — but 
brought on the specter of global annihilation. It 
created a superpower struggle — yet it also ulti- 
mately helped bring about the end of Soviet 
totalitarianism, thus opening the way for a 
greater level of peace and economic and cultural 
exchange than the world has ever known. Yet 
nuclear arsenals still remain, and the nuclear 
threat is far from over. 

So just what is this literally earth-shattering 
formula? E stands for rest energy, m for mass, and 
c for the speed of light, which is 186,000 mi 
(297,600 km) per second. Squared, this yields an 
almost unbelievably staggering number. 

VDLUME 2: REAL-LIFE PHYSICS 


1 79 



Energy 


Hence, even an object of insignificant mass 
possesses an incredible amount of rest energy. 
The baseball, for instance, weighs only about 
0.333 lb, which — on Earth, at least — converts to 
0.15 kg. (The latter is a unit of mass, as opposed 
to weight.) Yet when factored into the rest energy 
equation, it yields about 3.75 billion kilowatt- 
hours — enough to provide an American home 
with enough electrical power to last it more than 
156,000 years! 

How can a mere baseball possess such ener- 
gy? It is not the baseball in and of itself, but its 
mass; thus every object with mass of any kind 
possesses rest energy. Often, mass energy can be 
released in very small quantities through purely 
thermal or chemical processes: hence, when a fire 
burns, an almost infinitesimal portion of the 
matter that went into making the fire is convert- 
ed into energy. If a stick of dynamite that 
weighed 2.2 lb (1 kg) exploded, the portion of it 
that “disappeared” would be equal to 6 parts out 
of 100 billion; yet that portion would cause a 
blast of considerable proportions. 

As noted much earlier, the derivation of Ein- 
stein’s formula — and, more to the point, how he 
came to recognize the fundamental principles 
involved — is far beyond the scope of this essay. 
What is important is the fact, hypothesized by 
Einstein and confirmed in subsequent experi- 
ments, that matter is convertible to energy, a fact 
that becomes apparent when matter is accelerat- 
ed to speeds close to that of light. 

Physicists do not possess a means for pro- 
pelling a baseball to a speed near that of light — 
or of controlling its behavior and capturing its 


energy. Instead, atomic energy — whether of the 
wartime or peacetime varieties (that is, in power 
plants) — involves the acceleration of mere atom- 
ic particles. Nor is any atom as good as another. 
Typically physicists use uranium and other 
extremely rare minerals, and often, they further 
process these minerals in highly specialized ways. 
It is the rarity and expense of those minerals, 
incidentally — not the difficulty of actually put- 
ting atomic principles to work — that has kept 
smaller nations from developing their own 
nuclear arsenals. 

WHERE TD LEARN MDRE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Berger, Melvin. Sound, Heat and Light: Energy at Work. 
Illustrated by Anna DiVito. New York: Scholastic, 
1992. 

Gardner, Robert. Energy Projects for Young Scientists. New 
York: F. Watts, 1987. 

“Kinetic and Potential Energy” Thinkquest (Web site). 
<http://library.thinkquest.org/2745/data/ke.htm> 
(March 12,2001). 

Snedden, Robert. Energy. Des Plaines, IL: Heinemann, 
Library, 1999. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

“Work and Energy” (Web site). <http://www.glenbrook. 
kl2.il.us/gbssci/phys/Class/energy/energtoc.html> 
(March 12,2001). 

World of Coasters (Web site). <http://www. 
worldofcoasters.com> (March 12, 2001). 

Zubrowski, Bernie. Raceways: Having Fun with Balls and 
Tracks. Illustrated by Roy Doty. New York: Morrow, 
1985. 


| 1 SD 


VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


SCIENCE OF EVERYDAY THINGS 

REAL-LIFE PHYSICS 

THERMODYNAMICS 

GAS LAWS 
MOLECULAR DYNAMICS 
STRUCTURE DF MATTER 
THERMODYNAMICS 
H E AT 
T E M P E RAT U R E 
THERMAL EXPANSION 


1 B 1 




GAS 


LAWS 


C □ N C E PT 

Gases respond more dramatically to temperature 
and pressure than do the other three basic types 
of matter (liquids, solids and plasma). For gases, 
temperature and pressure are closely related to 
volume, and this allows us to predict their behav- 
ior under certain conditions. These predictions 
can explain mundane occurrences, such as the 
fact that an open can of soda will soon lose its 
fizz, but they also apply to more dramatic, life- 
and-death situations. 

H □ W IT WDRKS 

Ordinary air pressure at sea level is equal to 14.7 
pounds per square inch, a quantity referred to as 
an atmosphere (atm). Because a pound is a unit 
of force and a kilogram a unit of mass, the met- 
ric equivalent is more complex in derivation. 
A newton (N), or 0.2248 pounds, is the metric 
unit of force, and a pascal (Pa) — 1 newton per 
square meter — the unit of pressure. Hence, an 
atmosphere, expressed in metric terms, is 1.013 
X 10 5 Pa. 

Gases vs. Solids and Liq- 
uids: A Strikingly Different 
Response 

Regardless of the units you use, however, gases 
respond to changes in pressure and temperature 
in a remarkably different way than do solids or 
liquids. Using a small water sample, say, 0.2642 
gal ( 1 1), an increase in pressure from 1-2 atm will 
decrease the volume of the water by less than 
0.01%. A temperature increase from 32° to 212°F 
(0 to 100°C) will increase its volume by only 2% 
The response of a solid to these changes is even 

SCIENCE □ F EVERYDAY THINGS 


less dramatic; however, the reaction of air (a 
combination of oxygen, nitrogen, and other 
gases) to changes in pressure and temperature is 
radically different. 

For air, an equivalent temperature increase 
would result in a volume increase of 37%, and an 
equivalent pressure increase will decrease the 
volume by a whopping 50%. Air and other gases 
also have a boiling point below room tempera- 
ture, whereas the boiling point for water is high- 
er than room temperature and that of solids is 
much higher. The reason for this striking differ- 
ence in response can be explained by comparing 
all three forms of matter in terms of their overall 
structure, and in terms of their molecular behav- 
ior. (Plasma, a gas-like state found, for instance, 
in stars and comets’ tails, does not exist on Earth, 
and therefore it will not be included in the com- 
parisons that follow.) 

Mdlecular Structure Deter- 
mines Reaction 

Solids possess a definite volume and a definite 
shape, and are relatively noncompressible: for 
instance, if you apply extreme pressure to a steel 
plate, it will bend, but not much. Liquids have a 
definite volume, but no definite shape, and tend 
to be noncompressible. Gases, on the other hand, 
possess no definite volume or shape, and are 
compressible. 

At the molecular level, particles of solids 
tend to be definite in their arrangement and close 
in proximity — indeed, part of what makes a solid 
“solid,” in the everyday meaning of that term, is 
the fact that its constituent parts are basically 
immovable. Liquid molecules, too, are close in 
proximity, though random in arrangement. Gas 

VDLUME z: real-life physics 


1 S3 



□ as Laws 


| 1 B4 


molecules, too, are random in arrangement, but 
tend to be more widely spaced than liquid mole- 
cules. Solid particles are slow moving, and have a 
strong attraction to one another, whereas gas 
particles are fast-moving, and have little or no 
attraction. (Liquids are moderate in both 
regards.) 

Given these interesting characteristics of 
gases, it follows that a unique set of parameters — 
collectively known as the “gas laws” — are needed 
to describe and predict their behavior. Most of 
the gas laws were derived during the eighteenth 
and nineteenth centuries by scientists whose 
work is commemorated by the association of 
their names with the laws they discovered. These 
men include the English chemists Robert Boyle 
(1627-1691), John Dalton (1766-1844), and 
William Henry (1774-1836); the French physi- 
cists and chemists J. A. C. Charles (1746-1823) 
and Joseph Gay-Lussac (1778-1850), and the Ital- 
ian physicist Amedeo Avogadro (1776-1856). 

Bdyle’s, Charles’s, and Gay- 
Lussac’s Laws 

Boyle’s law holds that in isothermal conditions 
(that is, a situation in which temperature is kept 
constant), an inverse relationship exists between 
the volume and pressure of a gas. (An inverse 
relationship is a situation involving two vari- 
ables, in which one of the two increases in direct 
proportion to the decrease in the other.) In this 
case, the greater the pressure, the less the volume 
and vice versa. Therefore the product of the vol- 
ume multiplied by the pressure remains constant 
in all circumstances. 

Charles’s law also yields a constant, but in 
this case the temperature and volume are allowed 
to vary under isobarometric conditions — that is, 
a situation in which the pressure remains the 
same. As gas heats up, its volume increases, and 
when it cools down, its volume reduces accord- 
ingly. Hence, Charles established that the ratio of 
temperature to volume is constant. 

By now a pattern should be emerging: both 
of the aforementioned laws treat one parameter 
(temperature in Boyle’s, pressure in Charles’s) as 
unvarying, while two other factors are treated as 
variables. Both in turn yield relationships 
between the two variables: in Boyle’s law, pres- 
sure and volume are inversely related, whereas in 
Charles’s law, temperature and volume are 
directly related. 

VDLUME 2: REAL-LIFE PHYSICS 


In Gay-Lussac’s law, a third parameter, vol- 
ume, is treated as a constant, and the result is a 
constant ratio between the variables of pressure 
and temperature. According to Gay-Lussac’s law, 
the pressure of a gas is directly related to its 
absolute temperature. 

Absolute temperature refers to the Kelvin 
scale, established by William Thomson, Lord 
Kelvin (1824-1907). Drawing on Charles’s dis- 
covery that gas at 0°C (32°F) regularly contracted 
by about 1/273 of its volume for every Celsius 
degree drop in temperature, Thomson derived 
the value of absolute zero (-273.15°C or 
-459.67°F). Using the Kelvin scale of absolute 
temperature, Gay-Lussac found that at lower 
temperatures, the pressure of a gas is lower, while 
at higher temperatures its pressure is higher. 
Thus, the ratio of pressure to temperature is a 
constant. 

Avogadro’s Law 

Gay-Lussac also discovered that the ratio in 
which gases combine to form compounds can be 
expressed in whole numbers: for instance, water 
is composed of one part oxygen and two parts 
hydrogen. In the language of modern science, 
this would be expressed as a relationship between 
molecules and atoms: one molecule of water 
contains one oxygen atom and two hydrogen 
atoms. 

In the early nineteenth century, however, sci- 
entists had yet to recognize a meaningful distinc- 
tion between atoms and molecules. Avogadro 
was the first to achieve an understanding of the 
difference. Intrigued by the whole-number rela- 
tionship discovered by Gay-Lussac, Avogadro 
reasoned that one liter of any gas must contain 
the same number of particles as a liter of anoth- 
er gas. He further maintained that gas consists of 
particles — which he called molecules — that in 
turn consist of one or more smaller particles. 

In order to discuss the behavior of mole- 
cules, it was necessary to establish a large quanti- 
ty as a basic unit, since molecules themselves are 
very small. For this purpose, Avogadro estab- 
lished the mole, a unit equal to 6.022137 X 10 23 
(more than 600 billion trillion) molecules. The 
term “mole” can be used in the same way we use 
the word “dozen.” Just as “a dozen” can refer to 
twelve cakes or twelve chickens, so “mole” always 
describes the same number of molecules. 

SCIENCE OF EVERYDAY THINGS 


Gas Laws 


Just as one liter of water, or one liter of mer- 
cury, has a certain mass, a mole of any given sub- 
stance has its own particular mass, expressed in 
grams. The mass of one mole of iron, for 
instance, will always be greater than that of one 
mole of oxygen. The ratio between them is exact- 
ly the same as the ratio of the mass of one iron 
atom to one oxygen atom. Thus the mole makes 
if possible to compare the mass of one element or 
one compound to that of another. 

Avogadro’s law describes the connection 
between gas volume and number of moles. 
According to Avogadro’s law, if the volume of gas 
is increased under isothermal and isobarometric 
conditions, the number of moles also increases. 
The ratio between volume and number of moles 
is therefore a constant. 

The Ideal Gas Law 

Once again, it is easy to see how Avogadro’s law 
can be related to the laws discussed earlier, since 
they each involve two or more of the four param- 
eters: temperature, pressure, volume, and quanti- 
ty of molecules (that is, number of moles). In 
fact, all the laws so far described are brought 
together in what is known as the ideal gas law, 
sometimes called the combined gas law. 

The ideal gas law can be stated as a formula, 
p V = nRT, where p stands for pressure, V for vol- 
ume, n for number of moles, and T for tempera- 
ture. R is known as the universal gas constant, a 
figure equal to 0.0821 atm • liter/mole • K. (Like 
most terms in physics, this one is best expressed 
in metric rather than English units.) 

Given the equation pV = nRT and the fact 
that R is a constant, it is possible to find the value 
of any one variable — pressure, volume, number 
of moles, or temperature — as long as one knows 
the value of the other three. The ideal gas law also 
makes it possible to discern certain relations: 
thus if a gas is in a relatively cool state, the prod- 
uct of its pressure and volume is proportionately 
low; and if heated, its pressure and volume prod- 
uct increases correspondingly. Thus 


where p is the product of its initial pressure 
and its initial volume, T, its initial temperature, 

SCIENCE □ F EVERYDAY THINES 





A FIRE EXTINGUISHER CONTAINS A HIGH-PRESSURE MIX- 
TURE OF WATER AND CARBON DIOXIDE THAT RUSHES 
OUT OF THE SIPHON TUBE, WHICH IS OPENED WHEN THE 

release valve is depressed. (Photograph by Craig Lovell/ 
Corbis. Reproduced by permission.) 

p 2 V 2 the product of its final volume and final 
pressure, and T 2 its final temperature. 

Five Postulates Regarding 
THE BEHAVIGR DF GASES 

Five postulates can be applied to gases. These 
more or less restate the terms of the earlier dis- 
cussion, in which gases were compared to solids 
and liquids; however, now those comparisons 
can be seen in light of the gas laws. 

First, the size of gas molecules is minuscule 
in comparison to the distance between them, 
making gas highly compressible. In other words, 
there is a relatively high proportion of empty 
space between gas molecules. 

Second, there is virtually no force attracting 
gas molecules to one another. 

Third, though gas molecules move random- 
ly, frequently colliding with one another, their 
net effect is to create uniform pressure. 

VDLUME 2: REAL-LIFE PHYSICS 


1 B5 



Gas Laws 



A HOT-AIR BALLOON FLOATS BECAUSE THE AIR INSIDE IT IS NOT AS DENSE THAN THE AIR OUTSIDE. THE WAY IN 
WHICH THE DENSITY OF THE AIR IN THE BALLOON IS REDUCED REFLECTS THE GAS LAWS. (Duomo/Corbis. Reproduced by 

permission.) 


| 1 B S 


Fourth, the elastic nature of the collisions 
results in no net loss of kinetic energy, the ener- 
gy that an object possesses by virtue of its 
motion. If a stone is dropped from a height, it 

VOLUME 2: REAL-LIFE PHYSICS 


rapidly builds kinetic energy, but upon hitting a 
nonelastic surface such as pavement, most of that 
kinetic energy is transferred to the pavement. In 
the case of two gas molecules colliding, however, 

SCIENCE OF EVERYDAY THINGS 


they simply bounce off one another, only to col- 
lide with other molecules and so on, with no 
kinetic energy lost. 

Fifth, the kinetic energy of all gas molecules 
is directly proportional to the absolute tempera- 
ture of the gas. 

Laws of Partial Pressure 

Two gas laws describe partial pressure. Dalton’s 
law of partial pressure states that the total 
pressure of a gas is equal to the sum of its par 
tial pressures — that is, the pressure exerted 
by each component of the gas mixture. As 
noted earlier, air is composed mostly of nitrogen 
and oxygen. Along with these are small compo- 
nents carbon dioxide and gases collectively 
known as the rare or noble gases: argon, helium, 
krypton, neon, radon, and xenon. Hence, the 
total pressure of a given quantity of air is equal to 
the sum of the pressures exerted by each of these 
gases. 

Henry’s law states that the amount of gas 
dissolved in a liquid is directly proportional to 
the partial pressure of the gas above the surface 
of the solution. This applies only to gases such as 
oxygen and hydrogen that do not react chemical- 
ly to liquids. On the other hand, hydrochloric 
acid will ionize when introduced to water: one or 
more of its electrons will be removed, and its 
atoms will convert to ions, which are either posi- 
tive or negative in charge. 

REAL-LIFE 
A P P L I C AT I □ N S 

Pressure Changes 

opening a soda can. Inside a 
can or bottle of carbonated soda is carbon diox- 
ide gas (C0 2 ), most of which is dissolved in the 
drink itself. But some of it is in the space (some- 
times referred to as “head space”) that makes up 
the difference between the volume of the soft 
drink and the volume of the container. 

At the bottling plant, the soda manufacturer 
adds high-pressure carbon dioxide to the head 
space in order to ensure that more C0 2 will be 
absorbed into the soda itself. This is in accor- 
dance with Henry’s law: the amount of gas (in 
this case C0 2 ) dissolved in the liquid (soda) is 
directly proportional to the partial pressure of 

SCIENCE DF EVERYDAY THINGS 


the gas above the surface of the solution — that is, 
the C0 2 in the head space. The higher the pres- 
sure of the C0 2 in the head space, the greater the 
amount of C0 2 in the drink itself; and the greater 
the C0 2 in the drink, the greater the “fizz” of 
the soda. 

Once the container is opened, the pressure 
in the head space drops dramatically. Once again, 
Henry’s law indicates that this drop in pressure 
will be reflected by a corresponding drop in the 
amount of C0 2 dissolved in the soda. Over a 
period of time, the soda will release that gas, and 
will eventually go “flat.” 

FIRE E XT INGUISHERS. A fire 

extinguisher consists of a long cylinder with an 
operating lever at the top. Inside the cylinder is a 
tube of carbon dioxide surrounded by a quantity 
of water, which creates pressure around the C0 2 
tube. A siphon tube runs vertically along the 
length of the extinguisher, with one opening near 
the bottom of the water. The other end opens in 
a chamber containing a spring mechanism 
attached to a release valve in the C0 2 tube. 

The water and the C0 2 do not fill the entire 
cylinder: as with the soda can, there is “head 
space,” an area filled with air. When the operating 
lever is depressed, it activates the spring mecha- 
nism, which pierces the release valve at the top of 
the C0 2 tube. When the valve opens, the C0 2 
spills out in the “head space,” exerting pressure 
on the water. This high-pressure mixture of 
water and carbon dioxide goes rushing out of the 
siphon tube, which was opened when the release 
valve was depressed. All of this happens, of 
course, in a fraction of a second — plenty of time 
to put out the fire. 

aergsdl cans. Aerosol cans are 
similar in structure to fire extinguishers, though 
with one important difference. As with the fire 
extinguisher, an aerosol can includes a nozzle 
that depresses a spring mechanism, which in turn 
allows fluid to escape through a tube. But instead 
of a gas cartridge surrounded by water, most of 
the can’s interior is made up of the product (for 
instance, deodorant), mixed with a liquid pro- 
pellant. 

The “head space” of the aerosol can is filled 
with highly pressurized propellant in gas form, 
and in accordance with Henry’s law, a correspon- 
ding proportion of this propellant is dissolved in 
the product itself. When the nozzle is depressed, 

VDLUME 2: REAL-LIFE PHYSICS 


GAS LAWS 


1 37 


□ as Laws 


| 1 BS 


the pressure of the propellant forces the product 
out through the nozzle. 

A propellant, as its name implies, propels the 
product itself through the spray nozzle when the 
latter is depressed. In the past, chlorofluorocar- 
bons (CFCs) — manufactured compounds con- 
taining carbon, chlorine, and fluorine atoms — 
were the most widely used form of propellant. 
Concerns over the harmful effects of CFCs on the 
environment, however, has led to the develop- 
ment of alternative propellants, most notably 
hydrochlorofluorocarbons (FICFCs), CFC-like 
compounds that also contain hydrogen atoms. 

When the Temperature 
Changes 

A number of interesting things, some of them 
unfortunate and some potentially lethal, occur 
when gases experience a change in temperature. 
In these instances, it is possible to see the gas 
laws — particularly Boyle’s and Charles’s — 
at work. 

There are a number of examples of the dis- 
astrous effects that result from an increase in the 
temperature of a product containing com- 
bustible gases, as with natural gas and petrole- 
um-based products. In addition, the pressure on 
the gases in aerosol cans makes the cans highly 
explosive — so much so that discarded cans at a 
city dump may explode on a hot summer day. Yet 
there are other instances when heating a gas can 
produce positive effects. 

A hot-air balloon, for instance, floats 
because the air inside it is not as dense than the 
air outside. By itself, this fact does not depend on 
any of the gas laws, but rather reflects the concept 
of buoyancy. However, the way in which the den- 
sity of the air in the balloon is reduced does 
indeed reflect the gas laws. 

According to Charles’s law, heating a gas will 
increase its volume. Also, as noted in the first and 
second propositions regarding the behavior of 
gases, gas molecules are highly nonattractive to 
one another, and therefore, there is a great deal of 
space between them. The increase in volume 
makes that space even greater, leading to a signif- 
icant difference in density between the air in the 
balloon and the air outside. As a result, the bal- 
loon floats, or becomes buoyant. 

Although heating a gas can be beneficial, 
cooling a gas is not always a wise idea. If someone 

VDLUME 2: REAL-LIFE PHYSICS 


were to put a bag of potato chips into a freezer, 
thinking this would preserve their flavor, he 
would be in for a disappointment. Much of what 
maintains the flavor of the chips is the pressur- 
ization of the bag, which ensures a consistent 
internal environment in which preservative 
chemicals, added during the manufacture of the 
chips, can keep them fresh. Placing the bag in the 
freezer causes a reduction in pressure, as per Gay- 
Lussac’s law, and the bag ends up a limp version 
of its earlier self. 

Propane tanks and tires offer an example of 
the pitfalls that may occur by either allowing a 
gas to heat up or cool down by too much. 
Because most propane tanks are made according 
to strict regulations, they are generally safe, but it 
is not entirely inconceivable that an extremely 
hot summer day could cause a defective tank to 
burst. Certainly the laws of physics are there: an 
increase in temperature leads to an increase in 
pressure, in accordance with Gay-Lussac’s law, 
and could lead to an explosion. 

Because of the connection between heat and 
pressure, propane trucks on the highways during 
the summer are subjected to weight tests to 
ensure that they are not carrying too much of the 
gas. On the other hand, a drastic reduction in 
temperature could result in a loss in gas pressure. 
If a propane tank from Florida were transported 
by truck during the winter to northern Canada, 
the pressure would be dramatically reduced by 
the time it reached its destination. 

□ as Reactions That Move 
and Stop a Car 

In operating a car, we experience two examples of 
gas laws in operation. One of these, common to 
everyone, is that which makes the car run: the 
combustion of gases in the engine. The other is, 
fortunately, a less frequent phenomenon — but it 
can and does save lives. This is the operation of 
an air bag, which, though it is partly related to 
laws of motion, depends also on the behaviors 
explained in Charles’s law. 

With regard to the engine, when the driver 
pushes down on the accelerator, this activates a 
throttle valve that sprays droplets of gasoline 
mixed with air into the engine. (Older vehicles 
used a carburetor to mix the gasoline and air, but 
most modern cars use fuel-injection, which 
sprays the air-gas combination without requiring 
an intermediate step.) The mixture goes into the 

SCIENCE OF EVERYDAY THINGS 


Gas Laws 


Air bog 
container 


Steering 

wheel 



Inflated 
air bog 


In case gf a car collision, a sensor triggers the air bag to inflate rapidly with nitrogen gas. Before 
your body reaches the bag, however, it has already begun deflating. (Illustration by Hans & Cassidy. The Gale 
Group.) 


cylinder, where the piston moves up, compress- 
ing the gas and air. 

While the mixture is still compressed (high 
pressure, high density), an electric spark plug 
produces a flash that ignites it. The heat from this 
controlled explosion increases the volume of air, 
which forces the piston down into the cylinder. 
This opens an outlet valve, causing the piston to 
rise and release exhaust gases. 

As the piston moves back down again, an 
inlet valve opens, bringing another burst of gaso- 
line-air mixture into the chamber. The piston, 
whose downward stroke closed the inlet valve, 
now shoots back up, compressing the gas and air 
to repeat the cycle. The reactions of the gasoline 

SCIENCE □ E EVERYDAY THINGS 


and air are what move the piston, which turns a 
crankshaft that causes the wheels to rotate. 

So much for moving — what about stopping? 
Most modern cars are equipped with an airbag, 
which reacts to sudden impact by inflating. This 
protects the driver and front-seat passenger, who, 
even if they are wearing seatbelts, may otherwise 
be thrown against the steering wheel or dash- 
board.. 

But an airbag is much more complicated 
than it seems. In order for it to save lives, it must 
deploy within 40 milliseconds (0.04 seconds). 
Not only that, but it has to begin deflating before 
the body hits it. An airbag does not inflate if a car 
simply goes over a bump; it only operates in sit- 

VDLUME 2: REAL-LIFE PHYSICS 


1 39 


□ as Laws 


KEY TERMS 


absolute temperature: Tem- 

perature in relation to absolute zero 
(-273.15°C or -459.67°F). Its unit is the 
Kelvin (K), named after William Thomson, 
Lord Kelvin (1824-1907), who created the 
scale. The Kelvin and Celsius scales are 
directly related; hence, Celsius tempera- 
tures can be converted to Kelvins (for 
which neither the word or symbol for 
“degree” are used) by adding 273.15. 

avogadro’s law: A statement, 

derived by the Italian physicist Amedeo 
Avogadro (1776-1856), which holds that as 
the volume of gas increases under isother- 
mal and isobarometric conditions, the 
number of molecules (expressed in terms 
of mole number), increases as well. Thus 
the ratio of volume to mole number is a 
constant. 

bdyle’s law: A statement, derived 

by English chemist Robert Boyle (1627- 


1691), which holds that for gases in 
isothermal conditions, an inverse relation- 
ship exists between the volume and pres- 
sure of a gas. This means that the greater 
the pressure, the less the volume and vice 
versa, and therefore the product of pres- 
sure multiplied by volume yields a constant 
figure. 

Charles’s law: A statement, 

derived by French physicist and chemist 
J. A. C. Charles (1746-1823), which holds 
that for gases in isobarometric conditions, 
the ratio between the volume and temper- 
ature of a gas is constant. This means that 
the greater the temperature, the greater the 
volume and vice versa. 

DALTGN’S LAW DF PARTIAL PRES- 
SURE: A statement, derived by the 

English chemist lohn Dalton (1766-1844), 
which holds that the total pressure of a gas 
is equal to the sum of its partial pres- 


| i gp 


uations when the vehicle experiences extreme 
deceleration. When this occurs, there is a rapid 
transfer of kinetic energy to rest energy, as with 
the earlier illustration of a stone hitting concrete. 
And indeed, if you were to smash against a fully 
inflated airbag, it would feel like hitting con- 
crete — with all the expected results. 

The airbag’s sensor contains a steel ball 
attached to a permanent magnet or a stiff spring. 
The spring holds it in place through minor 
mishaps in which an airbag would not be war- 
ranted — for instance, if a car were simply to be 
“tapped” by another in a parking lot. But in a case 
of sudden deceleration, the magnet or spring 
releases the ball, sending it down a smooth bore. 
It flips a switch, turning on an electrical circuit. 
This in turn ignites a pellet of sodium azide, 
which fills the bag with nitrogen gas. 

VDLUME 2: REAL-LIFE PHYSICS 


The events described in the above illustra- 
tion take place within 40 milliseconds — less time 
than it takes for your body to come flying for- 
ward; and then the airbag has to begin deflating 
before the body reaches it. At this point, the high- 
ly pressurized nitrogen gas molecules begin 
escaping through vents. Thus as your body hits 
the bag, the deflation of the latter is moving it in 
the same direction that your body is going — only 
much, much more slowly. Two seconds after 
impact, which is an eternity in terms of the 
processes involved, the pressure inside the bag 
has returned to 1 atm. 

WHERE T El LEARN MDRE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Chemistry Units: Gas Laws.” (Web site). 

<http://bio.bio.rpi.edu/MS99/ausemaW/chem/gases. 
hmtl> (February 21, 2001). 

SCIENCE GF EVERYDAY THINGS 



Gas Laws 


KEY TERMS continued 


sures — that is, the pressure exerted by each 
component of the gas mixture. 

gay-lussac’s law: A statement, 

derived by the French physicist and 
chemist Joseph Gay-Lussac (1778-1850), 
which holds that the pressure of a gas is 
directly related to its absolute temperature. 
Hence the ratio of pressure to absolute 
temperature is a constant. 

henry’s law: A statement, derived 

by the English chemist William Henry 
(1774-836), which holds that the amount 
of gas dissolved in a liquid is directly pro- 
portional to the partial pressure of the gas 
above the solution. This holds true only for 
gases, such as hydrogen and oxygen, that 
are capable of dissolving in water without 
undergoing ionization. 

ideal gas law: A proposition, also 

known as the combined gas law, that draws 
on all the gas laws. The ideal gas law can be 


expressed as the formula pV = nRT, where 
p stands for pressure, V for volume, n for 
number of moles, and T for temperature. R 
is known as the universal gas constant, a 
figure equal to 0.0821 atm • liter/mole • K. 

inverse relationship: A situa- 

tion involving two variables, in which one 
of the two increases in direct proportion to 
the decrease in the other. 

ionization: A reaction in which an 

atom or group of atoms loses one or more 
electrons. The atoms are then converted to 
ions, which are either wholly positive or 
negative in charge. 

isothermal: Referring to a situa- 

tion in which temperature is kept constant. 

isobarometric: Referring to a sit- 

uation in which pressure is kept constant. 

mole: A unit equal to 6.022137 X 10 23 

molecules. 


Laws of Gases. New York: Arno Press, 1981. “Tutorials — 6.” <http://www.chemistrycoach.com/tutori- 

Macaulay, David. The New Way Things Work. Boston: a ^ s 6-html> (F e b mar y 2001). 

Houghton Mifflin, 1998. 

Mebane, Robert C. and Thomas R. Rybolt. Air and Other 
Gases. Illustrations by Anni Matsick. New York: 

Twenty-First Century Books, 1995. 


1 9 1 


SCIENCE OF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 



MOLECULAR DYNAMICS 


C □ N C E PT 

Physicists study matter and motion, or matter in 
motion. These forms of matter may be large, or 
they may be far too small to be seen by the most 
high-powered microscopes available. Such is the 
realm of molecular dynamics, the study and sim- 
ulation of molecular motion. As its name sug- 
gests, molecular dynamics brings in aspects of 
dynamics, the study of why objects move as they 
do, as well as thermodynamics, the study of the 
relationships between heat, work, and energy. 
Existing at the borders between physics and 
chemistry, molecular dynamics provides under- 
standing regarding the properties of matter — 
including phenomena such as the liquefaction of 
gases, in which one phase of matter is trans- 
formed into another. 

H □ W IT WORKS 

Molecules 

The physical world is made up of matter, physical 
substance that has mass; occupies space; is com- 
posed of atoms; and is, ultimately, convertible to 
energy. On Earth, three principal phases of mat- 
ter exist, namely solid, liquid, and gas. The differ- 
ences between these three are, on the surface at 
least, easily perceivable. Clearly, water is a liquid, 
just as ice is a solid and steam a gas. Yet, the ways 
in which various substances convert between 
phases are often complex, as are the interrela- 
tions between these phases. Ultimately, under- 
standing of the phases depends on an awareness 
of what takes place at the molecular level. 

An atom is the smallest particle of a chemi- 
cal element. It is not, however, the smallest thing 

VOLUME 2: REAL-LIFE PHYSICS 


in the universe; atoms are composed of subatom- 
ic particles, including protons, neutrons, and 
electrons. These subatomic particles are dis- 
cussed in the context of the structure of matter 
elsewhere in this volume, where they are exam- 
ined largely with regard to their electromagnetic 
properties. In the present context, the concern is 
primarily with the properties of atomic and 
molecular particles, in terms of mechanics, the 
study of bodies in motion, and thermodynamics. 

An atom must, by definition, represent one 
and only one chemical element, of which 109 
have been identified and named. It should be 
noted that the number of elements changes with 
continuing research, and that many of the ele- 
ments, particularly those discovered relatively 
recently — as, for instance, meitnerium (No. 109), 
isolated in the 1990s — are hardly part of every- 
day experience. So, perhaps 100 would be a bet- 
ter approximation; in any case, consider the mul- 
titude of possible ways in which the elements can 
be combined. 

Musicians have only seven tones at their dis- 
posal, and artists only seven colors — yet they 
manage to create a seemingly infinite variety of 
mutations in sound and sight, respectively. There 
are only 10 digits in the numerical system that 
has prevailed throughout the West since the late 
Middle Ages, yet it is possible to use that system 
to create such a range of numbers that all the 
books in all the libraries in the world could not 
contain them. This gives some idea of the range 
of combinations available using the hundred- 
odd chemical elements nature has provided — in 
other words, the number of possible molecular 
combinations that exist in the universe. 

SCIENCE □ F EVERYDAY THINGS 




This huge LiquEFiED natural gas container will be installed on a ship. The volume of the liquefied gas 

IS FAR LESS THAN IT WOULD BE IF THE GAS WERE IN A VAPORIZED STATE, THUS ENABLING EASE AND ECONOMY IN 

tr a n s p o rt. (Photograph by James L. Amos/Corbis. Reproduced by permission.) 


THE STRUCTURE OF MOLE- 

c u l e s . A molecule is a group of atoms 
joined in a single structure. Often, these atoms 
come from different elements, in which case the 
molecule represents a particular chemical com- 
pound, such as water, carbon dioxide, sodium 
chloride (salt), and so on. On the other hand, a 
molecule may consist only of one type of atom: 
oxygen molecules, for instance, are formed by the 
joining of two oxygen atoms. 

As much as scientists understand about mol- 
ecules and their structure, there is much that they 
do not know. Molecules of water are fairly easy to 
understand, because they have a simple, regular 
structure that does not change. A water molecule 
is composed of one oxygen atom joined by two 
hydrogen atoms, and since the oxygen atom is 
much larger than the two hydrogens, its shape 
can be compared to a basketball with two soft- 
balls attached. The scale of the molecule, of 
course, is so small as to boggle the mind: to bor- 
row an illustration from American physicist 
Richard Feynman (1918-1988), if a basketball 
were blown up to the size of Earth, the molecules 
inside of it would not even be as large as an ordi- 
nary-sized basketball. 

SCIENCE □ E EVERYDAY THINGS 


As for the water molecule, scientists know a 
number of things about it: the distance between 
the two hydrogen atoms (measured in units 
called an angstrom), and even the angle at which 
they join the oxygen atom. In the case of salt, 
however, the molecular structure is not nearly as 
uniform as that of water: atoms join together, but 
not always in regular ways. And then there are 
compounds far more complex than water or salt, 
involving numerous elements that fit together in 
precise and complicated ways. But, once that dis- 
cussion is opened, one has stepped from the 
realm of physics into that of chemistry, and that 
is not the intention here. Rather, the purpose of 
the foregoing and very cursory discussion of 
molecular structure is to point out that mole- 
cules are at the heart of all physical existence — 
and that the things we cannot see are every bit as 
complicated as those we can. 

the mdle. Given the tiny — to use an 
understatement — size of molecules, how do sci- 
entists analyze their behavior? Today, physicists 
have at their disposal electron microscopes and 
other advanced forms of equipment that make it 
possible to observe activity at the atomic and 
molecular levels. The technology that makes this 
possible is beyond the scope of the present dis- 

VDLUME 2: REAL-LIFE PHYSICS 


1 93 




HOW SMALL ARE MOLECULES? IF THIS BASKETBALL WERE BLOWN UP TO THE SIZE OF EARTH, THE MOLECULES INSIDE 

it would not be as big as a real basketball. (Photograph by Dimitri Iundt/Corbis. Reproduced by permission.) 


| 1 54 


cussion. On the other hand, consider a much 
simpler question: how do physicists weigh mole- 
cules? 

Obviously “a bunch” of iron (an element 
known by the chemical symbol Fe) weighs more 
than “a bunch” of oxygen, but what exactly is “a 
bunch”? Italian physicist Amedeo Avogadro 
(1776-1856), the first scientist to clarify the dis- 
tinction between atoms and molecules, created a 
unit that made it possible to compare the masses 
of various molecules. This is the mole, also 
known as “Avogadro’s number,” a unit equal to 
6.022137 X 10 23 (more than 600 billion trillion) 
molecules. 

The term “mole” can be used in the same 
way that the word “dozen” is used. Just as “a 
dozen” can refer to twelve cakes or twelve chick- 
ens, so “mole” always describes the same number 
of molecules. A mole of any given substance has 
its own particular mass, expressed in grams. The 
mass of one mole of iron, for instance, will always 
be greater than that of one mole of oxygen. The 
ratio between them is exactly the same as the 
ratio of the mass of one iron atom to one oxygen 
atom. Thus, the mole makes it possible to com- 
pare the mass of one element or compound to 
that of another. 

VOLUME 2: REAL-LIFE PHYSICS 


Molecular Attraction and 
M OTION 

Molecular dynamics can be understood primari- 
ly in terms of the principles of motion, identified 
by Sir Isaac Newton (1642-1727), principles that 
receive detailed discussion at several places in 
this volume. However, the attraction between 
particles at the atomic and molecular level can- 
not be explained by reference to gravitational 
force, also identified by Newton. For more than a 
century, gravity was the only type of force known 
to physicists, yet the pull of gravitation alone was 
too weak to account for the strong pull between 
atoms and molecules. 

During the eighteenth century and early 
nineteenth centuries, however, physicists and 
other scientists became increasingly aware of 
another form of interaction at work in the 
world — one that could not be explained in grav- 
itational terms. This was the force of electricity 
and magnetism, which Scottish physicist James 
Clerk Maxwell (1831-1879) suggested were dif- 
ferent manifestations of a “new” kind of force, 
electromagnetism. All subatomic particles pos- 
sess either a positive, negative, or neutral electri- 
cal charge. An atom usually has a neutral charge, 
meaning that it is composed of an equal number 
of protons (positive) and electrons (negative). In 

SCIENCE OF EVERYDAY THINGS 



certain situations, however, it may lose one or 
more electrons and, thus, acquire a net charge, 
making it an ion. 

Positive and negative charges attract one 
another, much as the north and south poles of 
two different magnets attract. (In fact, magnet- 
ism is simply an aspect of electromagnetic force.) 
Not only do the positive and negative elements of 
an atom attract one another, but positive ele- 
ments in atoms attract negative elements in other 
atoms, and vice versa. These interactions are 
much more complex than the preceding discus- 
sion suggests, of course; the important point is 
that a force other than gravitation draws matter 
together at the atomic and molecular levels. On 
the other hand, the interactions that are critical 
to the study of molecular dynamics are primari- 
ly mechanical, comprehensible from the stand- 
point of Newtonian dynamics. 

MOLECULAR BEHAVIOR AND 

phases of matter. All molecules are 
in motion, and the rate of that motion is affected 
by the attraction between them. This attraction 
or repulsion can be though of like a spring con- 
necting two molecules, an analogy that works 
best for solids, but in a limited way for liquids. 
Most molecular motion in liquids and gases is 
caused by collisions with other molecules; even 
in solids, momentum is transferred from one 
molecule to the next along the “springs,” but ulti- 
mately the motion is caused by collisions. Hence 
molecular collisions provide the mechanism by 
which heat is transferred between two bodies in 
contact. 

The rate at which molecules move in rela- 
tion to one another determines phase of mat- 
ter — that is, whether a particular item can be 
described as solid, liquid, or gas. The movement 
of molecules means that they possess kinetic 
energy, or the energy of movement, which is 
manifested as thermal energy and measured by 
temperature. Temperature is really nothing more 
than molecules in motion, relative to one anoth- 
er: the faster they move, the greater the kinetic 
energy, and the greater the temperature. 

When the molecules in a material move 
slowly in relation to one another, they tend to be 
close in proximity, and hence the force of attrac- 
tion between them is strong. Such a material is 
called a solid. In molecules of liquid, by contrast, 
the rate of relative motion is higher, so the mole- 
cules tend to be a little more spread out, and 

SCIENCE DF EVERYDAY THINGS 


therefore the force between them is weaker. A 
material substance whose molecules move at 
high speeds, and therefore exert little attraction 
toward one another, is known as a gas. All forms 
of matter possess a certain (very large) amount of 
energy due to their mass; thermal energy, howev- 
er, is — like phase of matter — a function of the 
attractions between particles. Hence, solids gen- 
erally have less energy than liquids, and liquids 
less energy than gases. 

REAL-LIFE 
A P P L I C AT I □ N S 

Kinetic Theories of Matter 

English chemist John Dalton (1766-1844) was 
the first to recognize that nature is composed of 
tiny particles. In putting forward his idea, Dalton 
adopted a concept from the Greek philosopher 
Democritus (c. 470-380 B.c.), who proposed that 
matter is made up of tiny units he called atomos, 
or “indivisible.” 

Dalton recognized that the structure of 
atoms in a particular element or compound is 
uniform, and maintained that compounds are 
made up of compound atoms: in other words, 
that water, for instance, is composed of “water 
atoms.” Soon after Dalton, however, Avogadro 
clarified the distinction between atoms and mol- 
ecules. Neither Dalton nor Avogadro offered 
much in the way of a theory regarding atomic or 
molecular behavior; but another scientist had 
already introduced the idea that matter at the 
smallest levels is in a constant state of motion. 

This was Daniel Bernoulli (1700-1782), a 
Swiss mathematician and physicist whose studies 
of fluids — a term which encompasses both gases 
and liquids — provided a foundation for the field 
of fluid mechanics. (Today, Bernoulli’s principle, 
which relates the velocity and pressure of fluids, 
is applied in the field of aerodynamics, and 
explains what keeps an airplane aloft.) Bernoulli 
published his fluid mechanics studies in Hydro- 
dynamica (1700-1782), a work in which he pro- 
vided the basis for what came to be known as the 
kinetic theory of gases. 

brownian motion. Because he 
came before Dalton and Avogadro, and, thus, did 
not have the benefit of their atomic and molecu- 
lar theories, Bernoulli was not able to develop his 
kinetic theory beyond the seeds of an idea. The 

VDLUME 2: REAL-LIFE PHYSIGS 


MOLECULAR 

DYNAMICS 


1 95 


Molecular 

Dynamics 


| 1 96 


subsequent elaboration of kinetic theory, which 
is applied not only to gases but (with somewhat 
less effectiveness) to liquids and solids, in fact, 
resulted from an accidental discovery. 

In 1827, Scottish botanist Robert Brown 
(1773-1858) was studying pollen grains under a 
microscope, when he noticed that the grains 
underwent a curious zigzagging motion in the 
water. The pollen assumed the shape of a colloid, 
a pattern that occurs when particles of one sub- 
stance are dispersed — but not dissolved — in 
another substance. Another example of a col- 
loidal pattern is a puff of smoke. 

At first, Brown assumed that the motion had 
a biological explanation — that is, that it resulted 
from life processes within the pollen — but later, 
he discovered that even pollen from long-dead 
plants behaved in the same way. He never under- 
stood what he was witnessing. Nor did a number 
of other scientists, who began noticing other 
examples of what came to be known as Brownian 
motion: the constant but irregular zigzagging of 
colloidal particles, which can be seen clearly 
through a microscope. 

MAXWELL, BDLTZMANN, AND 
THE MATURING DF KINETIC THE- 
ORY. A generation after Brown’s time, kinetic 
theory came to maturity through the work of 
Maxwell and Austrian physicist Ludwig E. Boltz- 
mann (1844-1906). Working independently, the 
two men developed a theory, later dubbed the 
Maxwell-Boltzmann theory of gases, which 
described the distribution of molecules in a gas. 
In 1859, Maxwell described the distribution of 
molecular velocities, work that became the foun- 
dation of statistical mechanics — the study of 
large systems — by examining the behavior of 
their smallest parts. 

A year later, in 1860, Maxwell published a 
paper in which he presented the kinetic theory of 
gases: the idea that a gas consists of numerous 
molecules, relatively far apart in space, which 
interact by colliding. These collisions, he pro- 
posed, are responsible for the production of ther- 
mal energy, because when the velocity of the 
molecules increases — as it does after collision — 
the temperature increases as well. Eight years 
later, in 1868, Boltzmann independently applied 
statistics to the kinetic theory, explaining the 
behavior of gas molecules by means of what 
would come to be known as statistical me- 
chanics. 

VDLUME 2: REAL-LIFE PHYSICS 


Kinetic theory offered a convincing explana- 
tion of the processes involved in Brownian 
motion. According to the kinetic view, what 
Brown observed had nothing to do with the 
pollen particles; rather, the movement of those 
particles was simply the result of activity on the 
part of the water molecules. Pollen grains are 
many thousands of times larger than water mol- 
ecules, but since there are so many molecules in 
even one drop of water, and their motion is so 
constant but apparently random, the water mol- 
ecules are bound to move a pollen grain once 
every few thousand collisions. 

In 1905, Albert Einstein (1879-1955) ana- 
lyzed the behavior of particles subjected to 
Brownian motion. His work, and the confirma- 
tion of his results by French physicist Jean Bap- 
tiste Perrin (1870-1942), finally put an end to any 
remaining doubts concerning the molecular 
structure of matter. The kinetic explanation of 
molecular behavior, however, remains a theory. 

Kinetic Theory and Gases 

Maxwell’s and Boltzmann’s work helped explain 
characteristics of matter at the molecular level, 
but did so most successfully with regard to gases. 
Kinetic theory fits with a number of behaviors 
exhibited by gases: their tendency to fill any con- 
tainer by expanding to fit its interior, for 
instance, and their ability to be easily com- 
pressed. 

This, in turn, concurs with the gas laws (dis- 
cussed in a separate essay titled “Gas Laws”) — for 
instance, Boyle’s law, which maintains that pres- 
sure decreases as volume increases, and vice 
versa. Indeed, the ideal gas law, which shows an 
inverse relationship between pressure and vol- 
ume, and a proportional relationship between 
temperature and the product of pressure and vol- 
ume, is an expression of kinetic theory. 

THE GAS LAWS ILLUSTRATED. 

The operations of the gas laws are easy to visual- 
ize by means of kinetic theory, which portrays 
gas molecules as though they were millions upon 
billions of tiny balls colliding at random. Inside a 
cube-shaped container of gas, molecules are col- 
liding with every possible surface, but the net 
effect of these collisions is the same as though the 
molecules were divided into thirds, each third 
colliding with opposite walls inside the cube. 

SCIENCE DF EVERYDAY THINGS 


If the cube were doubled in size, the mole- 
cules bouncing back and forth between two sets 
of walls would have twice as far to travel between 
each collision. Their speed would not change, but 
the time between collisions would double, thus, 
cutting in half the amount of pressure they 
would exert on the walls. This is an illustration of 
Boyle’s law: increasing the volume by a factor of 
two leads to a decrease in pressure to half of its 
original value. 

On the other hand, if the size of the contain- 
er were decreased, the molecules would have less 
distance to travel from collision to collision. This 
means they would be colliding with the walls 
more often, and, thus, would have a higher 
degree of energy — and, hence, a higher tempera- 
ture. This illustrates another gas law, Charles’s 
law, which relates volume to temperature: as one 
of the two increases or decreases, so does the 
other. Thus, it can be said, in light of kinetic the- 
ory, that the average kinetic energy produced by 
the motions of all the molecules in a gas is pro- 
portional to the absolute temperature of the gas. 

GASES AND ABSOLUTE TEM- 
PERATURE. The term “absolute tempera- 
ture” refers to the Kelvin scale, established by 
William Thomson, Lord Kelvin (1824-1907). 
Drawing on Charles’s discovery that gas at 0°C 
(32°F) regularly contracts by about 1/273 of its 
volume for every Celsius degree drop in temper- 
ature, Thomson derived the value of absolute 
zero (-273.15°C or -459.67°F). The Kelvin and 
Celsius scales are directly related; hence, Celsius 
temperatures can be converted to Kelvins by 
adding 273.15. 

The Kelvin scale measures temperature in 
relation to absolute zero, or OK. (Units in the 
Kelvin system, known as Kelvins, do not include 
the word or symbol for degree.) But what is 
absolute zero, other than a very cold tempera- 
ture? Kinetic theory provides a useful definition: 
the temperature at which all molecular move- 
ment in a gas ceases. But this definition requires 
some qualification. 

First of all, the laws of thermodynamics 
show the impossibility of actually reaching 
absolute zero. Second, the vibration of atoms 
never completely ceases: rather, the vibration of 
the average atom is zero. Finally, one element — 
helium — does not freeze, even at temperatures 
near absolute zero. Only the application of pres- 
sure will push helium past the freezing point. 

SCIENCE DF EVERYDAY THINGS 


Changes of Phase 

Kinetic theory is more successful when applied to 
gases than to liquids and solids, because liquid 
and solid molecules do not interact nearly as fre- 
quently as gas particles do. Nonetheless, the 
proposition that the internal energy of any sub- 
stance — gas, liquid, or solid — is at least partly 
related to the kinetic energies of its molecules 
helps explain much about the behavior of matter. 

The thermal expansion of a solid, for 
instance, can be clearly explained in terms of 
kinetic theory. As discussed in the essay on elas- 
ticity, many solids are composed of crystals, reg- 
ular shapes composed of molecules joined to one 
another, as though on springs. A spring that is 
pulled back, just before it is released, is an exam- 
ple of potential energy: the energy that an object 
possesses by virtue of its position. For a crys- 
talline solid at room temperature, potential ener- 
gy and spacing between molecules are relatively 
low. But as temperature increases and the solid 
expands, the space between molecules increas- 
es — as does the potential energy in the solid. 

An example of a liquid displaying kinetic 
behavior is water in the process of vaporization. 
The vaporization of water, of course, occurs in 
boiling, but water need not be anywhere near the 
boiling point to evaporate. In either case, the 
process is the same. Speeds of molecules in any 
substance are distributed along a curve, meaning 
that a certain number of molecules have speeds 
well below, or well above, the average. Those 
whose speeds are well above the average have 
enough energy to escape the surface, and once 
they depart, the average energy of the remaining 
liquid is less than before. As a result, evaporation 
leads to cooling. (In boiling, of course, the con- 
tinued application of thermal energy to the 
entire water sample will cause more molecules to 
achieve greater energy, even as highly energized 
molecules leave the surface of the boiling water 
as steam.) 

The Phase Diagram 

The vaporization of water is an example of a 
change of phase — the transition from one phase 
of matter to another. The properties of any sub- 
stance, and the points at which it changes phase, 
are plotted on what is known as a phase diagram. 
The latter typically shows temperature along the 
x-axis, and pressure along the y-axis. It is also 
possible to construct a phase diagram that plots 

VDLUME 2: REAL-LIFE PHYSIGS 


MOLECULAR 

DYNAMICS 


1 97 


Molecular 

Dynamics 


| 1 98 


volume against temperature, or volume against 
pressure, and there are even three-dimensional 
phase diagrams that measure the relationship 
between all three — volume, pressure, and tem- 
perature. Here we will consider the simpler two- 
dimensional diagram we have described. 

For simple substances such as water and car- 
bon dioxide, the solid form of the substance 
appears at a relatively low temperature, and at 
pressures anywhere from zero upward. The line 
between solids and liquids, indicating the tem- 
perature at which a solid becomes a liquid at any 
pressure above a certain level, is called the fusion 
curve. Though it appears to be a line, it is indeed 
curved, reflecting the fact that at high pressures, 
a solid well below the normal freezing point for 
that substance may be melted to create a liquid. 

Liquids occupy the area of the phase dia- 
gram corresponding to relatively high tempera- 
tures and high pressures. Gases or vapors, on the 
other hand, can exist at very low temperatures, 
but only if the pressure is also low. Above the 
melting point for the substance, gases exist at 
higher pressures and higher temperatures. Thus, 
the line between liquids and gases often looks 
almost like a 45° angle. But it is not a straight 
line, as its name, the vaporization curve, indi- 
cates. The curve of vaporization reflects the fact 
that at relatively high temperatures and high 
pressures, a substance is more likely to be a gas 
than a liquid. 

CRITICAL POINT AND SUBLI- 

m at i d n . There are several other interesting 
phenomena mapped on a phase diagram. One is 
the critical point, which can be found at a place 
of very high temperature and pressure along the 
vaporization curve. At the critical point, high 
temperatures prevent a liquid from remaining a 
liquid, no matter how high the pressure. At the 
same time, the pressure causes gas beyond that 
point to become more and more dense, but due 
to the high temperatures, it does not condense 
into a liquid. Beyond the critical point, the sub- 
stance cannot exist in anything other than the 
gaseous state. The temperature component of the 
critical point for water is 705. 2°F (374°C) — at 
218 atm, or 218 times ordinary atmospheric 
pressure. For helium, however, critical tempera- 
ture is just a few degrees above absolute zero. 
This is why helium is rarely seen in forms other 
than a gas. 

VDLUME 2: REAL-LIFE PHYSICS 


There is also a certain temperature and pres- 
sure, called the triple point, at which some sub- 
stances — water and carbon dioxide are exam- 
ples — will be a liquid, solid, and gas all at once. 
Another interesting phenomenon is the sublima- 
tion curve, or the line between solid and gas. At 
certain very low temperatures and pressures, a 
substance may experience sublimation, meaning 
that a gas turns into a solid, or a solid into a gas, 
without passing through a liquid stage. A well- 
known example of sublimation occurs when “dry 
ice,” which is made of carbon dioxide, vaporizes 
at temperatures above (-109. 3°F [-78.5°C] ). Car- 
bon dioxide is exceptional, however, in that it 
experiences sublimation at relatively high pres- 
sures, such as those experienced in everyday life: 
for most substances, the sublimation point 
occurs at such a low pressure point that it is sel- 
dom witnessed outside of a laboratory. 

Liquefaction of Gases 

One interesting and useful application of phase 
change is the liquefaction of gases, or the change 
of gas into liquid by the reduction in its molecu- 
lar energy levels. There are two important prop- 
erties at work in liquefaction: critical tempera- 
ture and critical pressure. Critical temperature is 
that temperature above which no amount of 
pressure will cause a gas to liquefy. Critical pres- 
sure is the amount of pressure required to lique- 
fy the gas at critical temperature. 

Gases are liquefied by one of three methods: 
( 1 ) application of pressure at temperatures below 
critical; (2) causing the gas to do work against 
external force, thus, removing its energy and 
changing it to the liquid state; or (3) causing the 
gas to do work against some internal force. The 
second option can be explained in terms of the 
operation of a heat engine, as explored in the 
Thermodynamics essay. 

In a steam engine, an example of a heat 
engine, water is boiled, producing energy in the 
form of steam. The steam is introduced to a 
cylinder, in which it pushes on a piston to drive 
some type of machinery. In pushing against the 
piston, the steam loses energy, and as a result, 
changes from a gas back to a liquid. 

As for the use of internal forces to cool a gas, 
this can be done by forcing the vapor through a 
small nozzle or porous plug. Depending on the 
temperature and properties of the gas, such an 

SCIENCE DF EVERYDAY THINGS 


Molecular 

Dynamics 


KEY TERMS 


absolute zero: The temperature, 

defined as OK on the Kelvin scale, at which 
the motion of molecules in a solid virtu- 
ally ceases. Absolute zero is equal to 
-459.67°F (-273.15°C). 
atom: The smallest particle of a chem- 

ical element. An atom can exist either 
alone or in combination with other atoms 
in a molecule. 

brownian motion: The constant 

but irregular zigzagging of colloidal parti- 
cles, which can be seen clearly through a 
microscope. The phenomenon is named 
after Scottish botanist Robert Brown 
(1773-1858), who first witnessed it but was 
not able to explain it. The behavior exhib- 
ited in Brownian motion provides evi- 
dence for the kinetic theory of matter. 
change of phase: The transition 

from one phase of matter to another. 

CHEMICAL COMPOUND: A Sub- 

stance made up of atoms of more than one 
chemical element. These atoms are usually 
joined in molecules. 

chemical element: A substance 

made up of only one kind of atom, 
c o llo i d: A pattern that occurs when 

particles of one substance are dispersed — 
but not dissolved — in another substance. A 
puff of smoke in the air is an example of a 
colloid, whose behavior is typically charac- 
terized by Brownian motion. 
critical point: A coordinate, plot- 

ted on a phase diagram, above which a sub- 
stance cannot exist in anything other than 
the gaseous state. Located at a position of 
very high temperature and pressure, the 
critical point marks the termination of the 
vaporization curve. 


dynamics: The study of why objects 

move as they do. Dynamics is an element 
of mechanics. 

fluid: Any substance, whether gas or 

liquid, which tends to flow, and which con- 
forms to the shape of its container. Unlike 
solids, fluids are typically uniform in 
molecular structure: for instance, one mol- 
ecule of water is the same as another water 
molecule. 

fusion curve: The boundary 

between solid and liquid for any given sub- 
stance, as plotted on a phase diagram. 

□ as: A phase of matter in which mole- 

cules exert little or no attraction toward 
one another, and, therefore, move at high 
speeds. 

heat: Internal thermal energy that 

flows from one body of matter to another. 

kelvin scale: Established by 

William Thomson, Lord Kelvin (1824- 
1907), the Kelvin scale measures tempera- 
ture in relation to absolute zero, or OK. 
(Units in the Kelvin system, known as 
Kelvins, do not include the word or symbol 
for degree.) The Kelvin and Celsius scales 
are directly related; hence, Celsius temper- 
atures can be converted to Kelvins by 
adding 273.15. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 

KINETIC THEORY GF GASES: The 

idea that a gas consists of numerous mole- 
cules, relatively far apart in space, which 
interact by colliding. These collisions are 
responsible for the production of thermal 
energy, because when the velocity of the 
molecules increases — as it does after colli- 
sion — the temperature increases as well. 


1 99 


SCIENCE DF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 



Molecular 

Dynamics 


KEY TERMS continued 


KINETIC THEDRY OF MATTER: The 

application of the kinetic theory of gases to 
all forms of matter. Since particles of liq- 
uids and solids move much more slowly 
than do gas particles, kinetic theory is not 
as successful in this regard; however, the 
proposition that the internal energy of any 
substance is at least partly related to the 
kinetic energies of its molecules helps 
explain much about the behavior of 
matter. 

liquid: A phase of matter in which 

molecules exert moderate attractions 
toward one another, and, therefore, move 
at moderate speeds. 

matter: Physical substance that has 

mass; occupies space; is composed of 
atoms; and is ultimately convertible to 
energy. There are several phases of matter, 
including solids, liquids, and gases. 

mechanics: The study of bodies in 

motion. 


mole: A unit equal to 6.022137 X 10 23 
(more than 600 billion trillion) molecules. 
Since their size makes it impossible to 
weigh molecules in relatively small quanti- 
ties; hence, the mole, devised by Italian 
physicist Amedeo Avogadro (1776-1856), 
facilitates comparisons of mass between 
substances. 

molecular dynamics: The study 

and simulation of molecular motion. 

molecule: A group of atoms, usual- 

ly of more than one chemical element, 
joined in a structure. 

phase diagram: A chart, plotted 

for any particular substance, identifying 
the particular phase of matter for that sub- 
stance at a given temperature and pressure 
level. A phase diagram usually shows tem- 
perature along the x-axis, and pressure 
along the y-axis. 

phases of matter: The various 

forms of material substance (matter), 


| 2 □ □ 


operation may be enough to remove energy suf- 
ficient for liquefaction to take place. Sometimes, 
the process must be repeated before the gas fully 
condenses into a liquid. 

HISTORICAL background. 

Like the steam engine itself, the idea of gas lique- 
faction is a product of the early Industrial Age. 
One of the pioneering figures in the field was the 
brilliant English physicist Michael Faraday 
(1791-1867), who liquefied a number of high- 
critical temperature gases, such as carbon 
dioxide. 

Half a century after Faraday, French physi- 
cist Louis Paul Cailletet (1832-1913) and Swiss 
chemist Raoul Pierre Pictet (1846-1929) devel- 
oped the nozzle and porous-plug methods of liq- 
uefaction. This, in turn, made it possible to liq- 

vglume z: real-life physics 


uefy gases with much lower critical temperatures, 
among them oxygen, nitrogen, and carbon 
monoxide. 

By the end of the nineteenth century, physi- 
cists were able to liquefy the gases with the low- 
est critical temperatures. James Dewar of Scot- 
land (1842-1923) liquefied hydrogen, whose crit- 
ical temperature is -399. 5°F (-239. 7°C). Some 
time later, Dutch physicist Heike Kamerlingh 
Onnes (1853-1926) successfully liquefied the gas 
with the lowest critical temperature of them all: 
helium, which, as mentioned earlier, becomes a 
gas at almost unbelievably low temperatures. Its 
critical temperature is -449. 9°F (-267. 7°C), or 
just 5.3K. 

A P P L I C AT IDNS DF GAS LIQ- 

u e fa c t i □ n . Liquefied natural gas (LNG) 

SCIENCE DF EVERYDAY THINGS 



Molecular 

Dynamics 


KEY TERMS continued 


which are defined primarily in terms of the 
behavior exhibited by their atomic or 
molecular structures. On Earth, three prin- 
cipal phases of matter exist, namely solid, 
liquid, and gas. 

potential energy: The energy an 

object possesses by virtue of its position. 

solid: A phase of matter in which 

molecules exert strong attractions toward 
one another, and, therefore, move slowly. 

statistical mechanics: A realm 

of the physical sciences devoted to the 
study of large systems by examining the 
behavior of their smallest parts. 

sublimation curve: The bound- 

ary between solid and gas for any given 
substance, as plotted on a phase diagram. 

s yste m : In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 


all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 

temperature: A measure of the 

average kinetic energy — or molecular 
translational energy in a system. Differ- 
ences in temperature determine the direc- 
tion of internal energy flow between two 
systems when heat is being transferred. 

thermal energy: Heat energy, a 

form of kinetic energy produced by the 
movement of atomic or molecular parti- 
cles. The greater the movement of these 
particles, the greater the thermal energy. 

thermodynamics: The study of 

the relationships between heat, work, and 
energy. 

vaporization curve: The bound- 

ary between liquid and gas for any given 
substance as plotted on a phase diagram. 


and liquefied petroleum gas (LPG), the latter a 
mixture of by-products obtained from petrole- 
um and natural gas, are among the examples of 
liquefied gas in daily use. In both cases, the vol- 
ume of the liquefied gas is far less than it would 
be if the gas were in a vaporized state, thus 
enabling ease and economy in transport. 

Liquefied gases are used as heating fuel for 
motor homes, boats, and homes or cabins in 
remote areas. Other applications of liquefied 
gases include liquefied oxygen and hydrogen in 
rocket engines, and liquefied oxygen and petrole- 
um used in welding. The properties of liquefied 
gases also figure heavily in the science of produc- 
ing and studying low-temperature environ- 
ments. In addition, liquefied helium is used in 
studying the behavior of matter at temperatures 
close to absolute zero. 

SCIENCE OF EVERYDAY THINGS 


A “New” Form of Matter? 

Physicists at a Colorado laboratory in 1995 
revealed a highly interesting aspect of atomic 
motion at temperatures approaching absolute 
zero. Some 70 years before, Einstein had predict- 
ed that, at extremely low temperatures, atoms 
would fuse to form one large “superatom.” This 
hypothesized structure was dubbed the Bose- 
Einstein Condensate after Einstein and Satyen- 
dranath Bose (1894-1974), an Indian physicist 
whose statistical methods contributed to the 
development of quantum theory. 

Because of its unique atomic structure, the 
Bose-Einstein Condensate has been dubbed a 
“new” form of matter. It represents a quantum 
mechanical effect, relating to a cutting-edge area 
of physics devoted to studying the properties of 

VDLUME 2: REAL-LIFE PHYSICS 


za l 



Molecular 

Dynamics 


subatomic particles and the interaction of matter 
with radiation. Thus it is not directly related to 
molecular dynamics; nonetheless, the Bose-Ein- 
stein Condensate is mentioned here as an exam- 
ple of the exciting work being performed at a 
level beyond that addressed by molecular 
dynamics. Its existence may lead to a greater 
understanding of quantum mechanics, and on 
an everyday level, the “superatom” may aid in 
the design of smaller, more powerful com- 
puter chips. 

WHERE TO LEARN MORE 

Cooper, Christopher. Matter. New York: DK Publishing, 
1999. 

“Kinetic Theory of Gases: A Brief Review” University of 
Virginia Department of Physics (Web site). 
<http://www.phys.virginia.edu/classes/252/kinetic_ 
theory.html> (April 15, 2001). 


“The Kinetic Theory Page” (Web site). 

<http://comp.uark.edu/~jgeabana/mol_dyn/> (April 
15, 2001). 

Medoff, Sol and John Powers. The Student Chemist 
Explores Atoms and Molecules. Illustrated by Nancy 
Lou Gahan. New York: R. Rosen Press, 1977. 

“Molecular Dynamics” (Web site). 

<http://www.biochem.vt.edu/courses/modeling/ 
molecular_dynamics.html> (April 15, 2001). 

“Molecular Simulation Molecular Dynamics Page” (Web 
site). 

<http://www.phy.bris.ac.uk/research/theory/simula- 
tion/md.html> (April 15,2001). 

Santrey, Laurence. Heat. Illustrated by Lloyd Birming- 
ham. Mahwah, NJ: Troll Associates, 1985. 

Strasser, Ben. Molecules in Motion. Illustrated by Vern 
Jorgenson. Pasadena, CA: Franklin Publications, 
1967. 

Van, Jon. “U.S. Scientists Create a ‘Superatom.’” Chicago 
Tribune, July 14, 1995, p. 3. 


| ZDZ 


VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


STRUCTURE 


□ F M ATT E R 


C □ N C E PT 

The physical realm is made up of matter. On 
Earth, matter appears in three clearly defined 
forms — solid, liquid, and gas — whose visible and 
perceptible structure is a function of behavior 
that takes place at the molecular level. Though 
these are often referred to as “states” of matter, it 
is also useful to think of them as phases of mat- 
ter. This terminology serves as a reminder that 
any one substance can exist in any of the three 
phases. Water, for instance, can be ice, liquid, or 
steam; given the proper temperature and pres- 
sure, it may be solid, liquid, and gas all at once! 
But the three definite earthbound states of mat- 
ter are not the sum total of the material world: in 
outer space a fourth phase, plasma, exists — and 
there may be still other varieties in the physical 
universe. 

H □ W IT WORKS 

Matter and Energy 

Matter can be defined as physical substance that 
has mass; occupies space; is composed of atoms; 
and is ultimately convertible to energy. A signifi- 
cant conversion of matter to energy, however, 
occurs only at speeds approaching that of the 
speed of light, a fact encompassed in the famous 
statement formulated by Albert Einstein (1879- 
1955), E = me 2 . 

Einstein’s formula means that every item 
possesses a quantity of energy equal to its mass 
multiplied by the squared speed of light. Given 
the fact that light travels at 186,000 mi (297,600 
km) per second, the quantities of energy avail- 


able from even a tiny object traveling at that 
speed are massive indeed. This is the basis for 
both nuclear power and nuclear weaponry, each 
of which uses some of the smallest particles in 
the known universe to produce results that are 
both amazing and terrifying. 

The forms of matter that most people expe- 
rience in their everyday lives, of course, are trav- 
eling at speeds well below that of the speed of 
light. Even so, transfers between matter and ener- 
gy take place, though on a much, much smaller 
scale. For instance, when a fire burns, only a tiny 
fraction of its mass is converted to energy. The 
rest is converted into forms of mass different 
from that of the wood used to make the fire. 
Much of it remains in place as ash, of course, but 
an enormous volume is released into the atmos- 
phere as a gas so filled with energy that it gener- 
ates not only heat but light. The actual mass con- 
verted into energy, however, is infinitesimal. 

CONSERVATION AND CON- 
VERSION. The property of energy is, at all 
times and at all places in the physical universe, 
conserved. In physics, “to conserve” something 
means “to result in no net loss of” that particular 
component — in this case, energy. Energy is never 
destroyed: it simply changes form. Hence, the 
conservation of energy, a law of physics stating 
that within a system isolated from all other out- 
side factors, the total amount of energy remains 
the same, though transformations of energy 
from one form to another take place. 

Whereas energy is perfectly conserved, mat- 
ter is only approximately conserved, as shown 
with the example of the fire. Most of the matter 
from the wood did indeed turn into more mat- 


SCIENCE DF EVERYDAY THINGS 


VDLUME Z: REAL-LIFE PHYSICS 


2U3 



Structure 
□ f Matter 



An iceberg floats because the density of ice is lower than water, while its volume is greater, making 
the iceberg buoyant. (Photograph by Ric Engenbright/Corbis. Reproduced by permission.) 


| 2D4 


ter — that is, vapor and ash. Yet, as also noted, a 
tiny quantity of matter — too small to be per- 
ceived by the senses — turned into energy. 

The conservation of mass holds that total 
mass is constant, and is unaffected by factors 
such as position, velocity, or temperature, in any 
system that does not exchange any matter with its 
environment. This, however, is a qualified state- 
ment: at speeds well below c (the speed of light), 
it is essentially true, but for matter approaching c 
and thus, turning into energy, it is not. 

VDLUME 2: REAL-LIFE PHYSICS 


Consider an item of matter moving at the 
speed of 100 mi (160 km)/sec. This is equal to 

360.000 MPH (576,000 km/h) and in terms of 
the speeds to which humans are accustomed, it 
seems incredibly fast. After all, the fastest any 
human beings have ever traveled was about 

25.000 MPH (40,000 km/h), in the case of the 
astronauts aboard Apollo 11 in May 1969, and the 
speed under discussion is more than 14 times 
greater. Yet 100 mi/ sec is a snail’s pace compared 
to c: in fact, the proportional difference between 
an actual snail’s pace and the speed of a human 

SCIENCE OF EVERYDAY THINGS 


walking is not as great. Yet even at this leisurely 
gait, equal to 0.00054c, a portion of mass equal to 
0.0001% (one-millionth of the total mass) con- 
verts to energy. 

Matter at the Atomic Level 

In his brilliant work Six Easy Pieces, American 
physicist Richard Feynman (1918-1988) asked 
his readers, “If, in some cataclysm, all of scientif- 
ic knowledge were to be destroyed, and only one 
sentence passed on to the next generations of 
creatures, what statement would contain the 
most information in the fewest words? I believe it 
is the atomic hypothesis (or the atomic fact, or 
whatever you wish to call it) that all things are 
made of atoms — little articles that move around 
in perpetual motion, attracting each other when 
they are a little distance apart, but repelling upon 
being squeezed into one another. In that sen- 
tence, you will see, there is an enormous amount 
of information about the world, if just a little 
imagination and thinking are applied.” 

Feynman went on to offer a powerful series 
of illustrations concerning the size of atoms rela- 
tive to more familiar objects: if an apple were 
magnified to the size of Earth, for instance, the 
atoms in it would each be about the size of a reg- 
ular apple. Clearly atoms and other atomic parti- 
cles are far too small to be glimpsed by even the 
most highly powered optical microscope. Yet, it is 
the behavior of particles at the atomic level that 
defines the shape of the entire physical world. 
Viewed from this perspective, it becomes easy to 
understand how and why matter is convertible to 
energy. Likewise, the interaction between atoms 
and other particles explains why some types 
of matter are solid, others liquid, and still 
others, gas. 

AT DMS AND MOLECULES. An 

atom is the smallest particle of a chemical ele- 
ment. It is not, however, the smallest particle in 
the universe; atoms are composed of subatomic 
particles, including protons, neutrons, and elec- 
trons. But at the subatomic level, it is meaning- 
less to refer to, for instance, “an oxygen electron”: 
electrons are just electrons. An atom, then, is the 
fundamental unit of matter. Most of the sub- 
stances people encounter in the world, however, 
are not pure elements, such as oxygen or iron; 
they are chemical compounds, in which atoms of 
more than one element join together to form 
molecules. 


One of the most well-known molecular 
forms in the world is water, or H 2 0, composed of 
two hydrogen atoms and one oxygen atom. The 
arrangement is extremely precise and never 
varies: scientists know, for instance, that the two 
hydrogen atoms join the oxygen atom (which is 
much larger than the hydrogen atoms) at an 
angle of 105° 3’. Other molecules are much more 
complex than those of water — some of them 
much, much more complex, which is reflected in 
the sometimes unwieldy names required to iden- 
tify their chemical components. 

ATOMIC AND MOLECULAR 

theory. The idea of atoms is not new. More 
than 24 centuries ago, the Greek philosopher 
Democritus (c. 470-380 b.c.) proposed that mat- 
ter is composed of tiny particles he called a tom- 
os, or “indivisible.” Democritus was not, however, 
describing matter in a concrete, scientific way: 
his “atoms” were idealized, philosophical con- 
structs, not purely physical units. 

Yet, he came amazingly close to identifying 
the fundamental structure of physical reality — 
much closer than any number of erroneous the- 
ories (such as the “four elements” of earth, air, 
fire, and water) that prevailed until modern 
times. English chemist John Dalton (1766-1844) 
was the first to identify what Feynman later 
called the “atomic hypothesis”: that nature is 
composed of tiny particles. In putting forward 
his idea, Dalton adopted Democritus’s word 
“atom” to describe these basic units. 

Dalton recognized that the structure of 
atoms in a particular element or compound is 
uniform. He maintained that compounds are 
made up of compound atoms: in other words, 
that water, for instance, is a compound of “water 
atoms.” Water, however, is not an element, and 
thus, it was necessary to think of its atomic com- 
position in a different way — in terms of mole- 
cules rather than atoms. Dalton’s contemporary 
Amedeo Avogadro (1776-1856), an Italian physi- 
cist, was the first scientist to clarify the distinc- 
tion between atoms and molecules. 

the m d l e . Obviously, it is impractical 
to weigh a single molecule, or even several thou- 
sand; what was needed, then, was a number large 
enough to make possible practical comparisons 
of mass. Hence, the mole, a quantity equal to 
“Avogadro’s number.” The latter, named after 
Avogadro though not derived by him, is equal to 
6.022137 x 10 23 (more than 600 billion trillion) 
molecules. 


Structure 
□ f Matter 


2 □ 5 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


Structure 
□ f Matter 


^206 


The term “mole” can be used in the same 
way that the word “dozen” is used. Just as “a 
dozen” can refer to twelve cakes or twelve chick- 
ens, so “mole” always describes the same number 
of molecules. A mole of any given substance has 
its own particular mass, expressed in grams. The 
mass of one mole of iron, for instance, will always 
be greater than that of one mole of oxygen. The 
ratio between them is exactly the same as the 
ratio of the mass of one iron atom to one oxygen 
atom. Thus, the mole makes it possible to com- 
pare the mass of one element or compound to 
that of another. 

BROWNIAN MOTION AND KI- 
NETIC theory. Contemporary to both 
Dalton and Avogadro was Scottish naturalist 
Robert Brown (1773-1858), who in 1827 stum- 
bled upon a curious phenomenon. While study- 
ing pollen grains under a microscope, Brown 
noticed that the grains underwent a curious 
zigzagging motion in the water. At first, he 
assumed that the motion had a biological expla- 
nation — that is, it resulted from life processes 
within the pollen — but later he discovered that 
even pollen from long-dead plants behaved in 
the same way. 

Brown never understood what he was wit- 
nessing. Nor did a number of other scientists, 
who began noticing other examples of what 
came to be known as Brownian motion: the con- 
stant but irregular zigzagging of particles in a 
puff of smoke, for instance. Later, however, Scot- 
tish physicist James Clerk Maxwell (1831-1879) 
and others were able to explain it by what came 
to be known as the kinetic theory of matter. 

The kinetic theory, which is discussed in 
depth elsewhere in this book, is based on the idea 
that molecules are constantly in motion: hence, 
the water molecules were moving the pollen 
grains Brown observed. Pollen grains are many 
thousands of times as large as water molecules, 
but there are so many molecules in just one 
drop of water, and their motion is so constant 
but apparently random, that they are bound 
to move a pollen grain once every few thousand 
collisions. 

GROWTH IN UNDERSTANDING 

the atom. Einstein, who was born the year 
Maxwell died, published a series of papers in 
which he analyzed the behavior of particles sub- 
jected to Brownian motion. His work, and the 
confirmation of his results by French physicist 

VDLUME 2: REAL-LIFE PHYSICS 


Jean Baptiste Perrin (1870-1942), finally put an 
end to any remaining doubts concerning the 
molecular structure of matter. 

It may seem amazing that the molecular and 
atomic ideas were still open to question in the 
early twentieth century; however, the vast major- 
ity of what is known today concerning the atom 
emerged after World War I. At the end of the 
nineteenth century, scientists believed the atom 
to be indivisible, but growing evidence concern- 
ing electrical charges in atoms brought with it the 
awareness that there must be something smaller 
creating those charges. 

Eventually, physicists identified protons and 
electrons, but the neutron, with no electrical 
charge, was harder to discover: it was not identi- 
fied until 1932. After that point, scientists were 
convinced that just three types of subatomic par- 
ticles existed. However, subsequent activity 
among physicists — particularly those in the field 
of quantum mechanics — led to the discovery of 
other elementary particles, such as the photon. 
However, in this discussion, the only subatomic 
particles whose behavior is reviewed are the pro- 
ton, electron, and neutron. 

Motion and Attraction in 
Atoms and Molecules 

At the molecular level, every item of matter in the 
world is in motion. This may be easy enough to 
imagine with regard to air or water, since both 
tend to flow. But what about a piece of paper, or 
a glass, or a rock? In fact, all molecules are in con- 
stant motion, and depending on the particular 
phase of matter, this motion may vary from a 
mere vibration to a high rate of speed. 

Molecular motion generates kinetic energy, 
or the energy of movement, which is manifested 
as heat or thermal energy. Indeed, heat is really 
nothing more than molecules in motion relative 
to one another: the faster they move, the greater 
the kinetic energy, and the greater the heat. 

The movement of atoms and molecules is 
always in a straight line and at a constant veloci- 
ty, unless acted upon by some outside force. In 
fact, the motion of atoms and molecules is con- 
stantly being interfered with by outside forces, 
because they are perpetually striking one anoth- 
er. These collisions cause changes in direction, 
and may lead to transfers of energy from one 
particle to another. 

SCIENCE DF EVERYDAY THINGS 


ELECTROMAGNETIC FORCE 

i n at o m s . The behavior of molecules can- 
not be explained in terms of gravitational force. 
This force, and the motions associated with it, 
were identified by Sir Isaac Newton ( 1642-1727), 
and Newton’s model of the universe seemed to 
answer most physical questions. Then in the late 
nineteenth century, Maxwell discovered a second 
kind of force, electromagnetism. (There are two 
other known varieties of force, strong and weak 
nuclear, which are exhibited at the subatomic 
level.) Electromagnetic force, rather than gravita- 
tion, explains the attraction between atoms. 

Several times up to this point, the subatom- 
ic particles have been mentioned but not 
explained in terms of their electrical charge, 
which is principal among their defining charac- 
teristics. Protons have a positive electrical charge, 
while neutrons exert no charge. These two types 
of particles, which make up the vast majority of 
the atom’s mass, are clustered at the center, or 
nucleus. Orbiting around this nucleus are elec- 
trons, much smaller particles which exert a nega- 
tive charge. 

Chemical elements are identified by the 
number of protons they possess. Hydrogen, first 
element listed on the periodic table of elements, 
has one proton and is thus identified as 1; car- 
bon, or element 6, has six protons, and so on. 

An atom usually has a neutral charge, mean- 
ing that it is composed of an equal number of 
protons or electrons. In certain situations, how- 
ever, it may lose one or more electrons and thus 
acquire a net charge. Such an atom is called an 
ion. But electrical charge, like energy, is con- 
served, and the electrons are not “lost” when an 
atom becomes an ion: they simply go elsewhere. 

MOLECULAR BEHAVIOR AND 

s tat e s o f m att e r . Positive and neg- 
ative charges interact at the molecular level in a 
way that can be compared to the behavior of 
poles in a pair of magnets. Just as two north poles 
or two south poles repel one another, so like 
charges — two positives, or two negatives — repel. 
Conversely, positive and negative charges exert 
an attractive force on one another similar to that 
of a north pole and south pole in contact. 

In discussing phases of matter, the attraction 
between molecules provides a key to distinguish- 
ing between states of matter. This is not to say 
one particular phase of matter is a particularly 
good conductor of electrical current, however. 

SCIENCE DF EVERYDAY THINGS 


For instance, certain solids — particularly metals 
such as copper — are extremely good conductors. 
But wood is a solid, too, and conducts electrical 
current poorly. 

The properties of various forms of matter, 
viewed from the larger electromagnetic picture, 
are a subject far beyond the scope of this essay. In 
any case, the electromagnetic properties of con- 
cern in the present instance are not the ones 
demonstrated at a macroscopic level — that is, in 
view of “the big picture.” Rather, the subject of 
the attractive force operating at the atomic or 
molecular levels has been introduced to show 
that certain types of material have a greater inter- 
molecular attraction. 

As previously stated, all matter is in motion. 
The relative speed of that motion, however, is a 
function of the attraction between molecules, 
which in turn defines a material according to one 
of the phases of matter. When the molecules in a 
material exert a strong attraction toward one 
another, they move slowly, and the material is 
called a solid. Molecules of liquid, by contrast, 
exert a moderate attraction and move at moder- 
ate speeds. A material substance whose molecules 
exert little or no attraction, and therefore, move 
at high speeds, is known as a gas. 

These comparisons of molecular speed and 
attraction, obviously, are relative. Certainly, it is 
easy enough in most cases to distinguish between 
one phase of matter and another, but there are 
some instances in which they overlap. Examples 
of these will follow, but first it is necessary to dis- 
cuss the phases of matter in the context of their 
behavior in everyday situations. 

REAL-LIFE 
A P P L I C AT I □ N S 

From Sdlid to Liquid 

The attractions between particles have a number 
of consequences in defining the phases of matter. 
The strong attractive forces in solids cause its 
particles to be positioned close together. This 
means that particles of solids resist attempts to 
compress them, or push them together. Because 
of their close proximity, solid particles are fixed 
in an orderly and definite pattern. As a result, a 
solid usually has a definite volume and shape. 

A crystal is a type of solid in which the con- 
stituent parts are arranged in a simple, definite 

VDLUME Z : REAL-LIFE PHYSIGS 


STRUCTURE 
□ F MATTER 


2 07 


Structure 
□ f Matter 


| 2 □ S 


geometric arrangement that is repeated in all 
directions. Metals, for instance, are crystalline 
solids. Other solids are said to be amorphous, 
meaning that they possess no definite shape. 
Amorphous solids — clay, for example — either 
possess very tiny crystals, or consist of several 
varieties of crystal mixed randomly. Still other 
solids, among them glass, do not contain crystals. 

VIBRATIONS AND FREEZING. 

Because of their strong attractions to one anoth- 
er, solid particles move slowly, but like all parti- 
cles of matter, they do move. Whereas the parti- 
cles in a liquid or gas move fast enough to be in 
relative motion with regard to one another, how- 
ever, solid particles merely vibrate from a fixed 
position. 

This can be shown by the example of a 
singer hitting a certain note and shattering a 
glass. Contrary to popular belief, the note does 
not have to be particularly high: rather, the note 
should be on the same wavelength as the vibra- 
tion of the glass. When this occurs, sound energy 
is transferred directly to the glass, which shatters 
because of the sudden net intake of energy. 

As noted earlier, the attraction and motion 
of particles in matter has a direct effect on heat 
and temperature. The cooler the solid, the slower 
and weaker the vibrations, and the closer the par- 
ticles are to one another. Thus, most types of 
matter contract when freezing, and their density 
increases. Absolute zero, or OK on the Kelvin scale 
of temperature — equal to -459.67°F (-273°C) — 
is the point at which vibration virtually stops. 
Note that the vibration virtually stops, but does 
not stop entirely. In any event, the lowest 
temperature actually achieved, at a Finnish 
nuclear laboratory in 1993, is 2.8 • 10- 10 K, or 
0.00000000028K — still above absolute zero. 

UNUSUAL CHARACTERISTICS 

□ f ice. The behavior of water at the freez- 
ing/melting point is interesting and exceptional. 
Above 39.2°F (4°C) water, like most substances, 
expands when heated. But between 32°F (0°C) 
and that temperature, however, it actually con- 
tracts. And whereas most substances become 
much denser with lowered temperatures, the 
density of water reaches its maximum at 39.2°F. 
Below that point, it starts to decrease again. 

Not only does the density of ice begin 
decreasing just before freezing, but its volume 
increases. This is the reason ice floats: its weight 
is less than that of the water it has displaced, and 

VDLUME 2: REAL-LIFE PHYSICS 


therefore, it is buoyant. Additionally, the buoyant 
qualities of ice atop very cold water explain why 
the top of a lake may freeze, but lakes rarely 
freeze solid — even in the coldest of inhabited 
regions. 

Instead of freezing from the bottom up, as it 
would if ice were less buoyant than the water, the 
lake freezes from the top down. Furthermore, ice 
is a poorer conductor of heat than water, and, 
thus, little of the heat from the water below 
escapes. Therefore, the lake does not freeze com- 
pletely — only a layer at the top — and this helps 
preserve animal and plant life in the body of 
water. On the other hand, the increased volume 
of frozen water is not always good for humans: 
when water in pipes freezes, it may increase in 
volume to the point where the pipe bursts. 

m e lt i n g . When heated, particles begin 
to vibrate more and more, and, therefore, move 
further apart. If a solid is heated enough, it loses 
its rigid structure and becomes a liquid. The tem- 
perature at which a solid turns into a liquid is 
called the melting point, and melting points are 
different for different substances. For the most 
part, however, solids composed of heavier parti- 
cles require more energy — and, hence, higher 
temperatures — to induce the vibrations neces- 
sary for freezing. Nitrogen melts at -346°F 
(-210°C), ice at 32°F (0°C), and copper at 1,985°F 
(1,085°C). The melting point of a substance, 
incidentally, is the same as its freezing point: the 
difference is a matter of orientation — that is, 
whether the process is one of a solid melting to 
become a liquid, or of a liquid freezing to become 
a solid. 

The energy required to change a solid to a 
liquid is called the heat of fusion. In melting, all 
the heat energy in a solid (energy that exists due 
to the motion of its particles) is used in breaking 
up the arrangement of crystals, called a lattice. 
This is why the water resulting from melted ice 
does not feel any warmer than when it was 
frozen: the thermal energy has been expended, 
with none left over for heating the water. Once all 
the ice is melted, however, the absorbed energy 
from the particles — now moving at much greater 
speeds than when the ice was in a solid state — 
causes the temperature to rise. 

Frdm Liquid to Gas 

The particles of a liquid, as compared to those of 
a solid, have more energy, more motion, and less 

science df everyday things 


attraction to one another. The attraction, how- 
ever, is still fairly strong: thus, liquid particles are 
in close enough proximity that the liquid resists 
compression. 

On the other hand, their arrangement is 
loose enough that the particles tend to move 
around one another rather than merely vibrating 
in place, as solid particles do. A liquid is therefore 
not definite in shape. Both liquids and gases tend 
to flow, and to conform to the shape of their con- 
tainer; for this reason, they are together classified 
as fluids. 

Owing to the fact that the particles in a liq- 
uid are not as close in proximity as those of a 
solid, liquids tend to be less dense than solids. 
The liquid phase of substance is thus inclined to 
be larger in volume than its equivalent in solid 
form. Again, however, water is exceptional in this 
regard: liquid water actually takes up less space 
than an equal mass of frozen water. 

boiling. When a liquid experiences an 
increase in temperature, its particles take on 
energy and begin to move faster and faster. They 
collide with one another, and at some point the 
particles nearest the surface of the liquid acquire 
enough energy to break away from their neigh- 
bors. It is at this point that the liquid becomes a 
gas or vapor. 

As heating continues, particles throughout 
the liquid begin to gain energy and move faster, 
but they do not immediately transform into gas. 
The reason is that the pressure of the liquid, 
combined with the pressure of the atmosphere 
above the liquid, tends to keep particles in place. 
Those particles below the surface, therefore, 
remain where they are until they acquire enough 
energy to rise to the surface. 

The heated particle moves upward, leaving 
behind it a hollow space — a bubble. A bubble is 
not an empty space: it contains smaller trapped 
particles, but its small weight relative to that of 
the liquid it disperses makes it buoyant. There- 
fore, a bubble floats to the top, releasing its 
trapped particles as gas or vapor. At that point, 
the liquid is said to be boiling. 

THE EFFECT DF ATMOSPHER- 
IC pressure. As they rise, the particles 
thus have to overcome atmospheric pressure, and 
this means that the boiling point for any liquid 
depends in part on the pressure of the surround- 
ing air. This is why cooking instructions often 
vary with altitude: the greater the distance from 

SCIENCE CF EVERYDAY THINGS 


sea level, the less the air pressure, and the shorter 
the required cooking time. 

Atop Mt. Everest, Earth’s highest peak at 
about 29,000 ft (8,839 m) above sea level, the 
pressure is approximately one-third normal 
atmospheric pressure. This means the air is one- 
third as dense as it is as sea level, which explains 
why mountain-climbers on Everest and other tall 
peaks must wear oxygen masks to stay alive. It 
also means that water boils at a much lower tem- 
perature on Everest than it does elsewhere. At sea 
level, the boiling point of water is 212°F (100°C), 
but at 29,000 ft it is reduced by one-quarter, to 
158°F (70°C). 

Of course, no one lives on the top of Mt. 
Everest — but people do live in Denver, Colorado, 
where the altitude is 5,577 ft (1,700 m) and the 
boiling point of water is 203°F (95°C). Given the 
lower boiling point, one might assume that food 
would cook faster in Denver than in New York, 
Los Angeles, or some other city close to sea level. 
In fact, the opposite is true: because heated parti- 
cles escape the water so much faster at high alti- 
tudes, they do not have time to acquire the ener- 
gy needed to raise the temperature of the water. 
It is for this reason that a recipe may contain a 
statement such as “at altitudes above XX feet, add 
XX minutes to cooking time.” 

If lowered atmospheric pressure means a 
lowered boiling point, what happens in outer 
space, where there is no atmospheric pressure? 
Liquids boil at very, very low temperatures. This 
is one of the reasons why astronauts have to wear 
pressurized suits: if they did not, their blood 
would boil — even though space itself is incredi- 
bly cold. 

LIQUID TD GAS AND BACK 

again. Note that the process of a liquid 
changing to a gas is similar to what occurs when 
a solid changes to a liquid: particles gain heat and 
therefore energy, begin to move faster, break free 
from one another, and pass a certain threshold 
into a new phase of matter. And just as the freez- 
ing and melting point for a given substance are 
the same temperature, the only difference being 
one of orientation, the boiling point of a liquid 
transforming into a gas is the same as the con- 
densation point for a gas turning into a liquid. 

The behavior of water in boiling and con- 
densation makes possible distillation, one of the 
principal methods for purifying seawater in vari- 
ous parts of the world. First, the water is boiled, 

VDLUME 2: REAL-LIFE PHYSIGS 


STRUCTURE 
□ F MATTER 


2D9 


Structure 
□ f Matter 


| 2 1 □ 


then, it is allowed to cool and condense, thus 
forming water again. In the process, the water 
separates from the salt, leaving it behind in the 
form of brine. A similar separation takes place 
when salt water freezes: because salt, like most 
solids, has a much lower freezing point than 
water, very little of it remains joined to the water 
in ice. Instead, the salt takes the form of a briny 
slush. 

□ as and its laws. Having 
reached the gaseous state, a substance takes on 
characteristics quite different from those of a 
solid, and somewhat different from those of a liq- 
uid. Whereas liquid particles exert a moderate 
attraction to one another, particles in a gas exert 
little to no attraction. They are thus free to move, 
and to move quickly. The shape and arrangement 
of gas is therefore random and indefinite — and, 
more importantly, the motion of gas particles 
give it much greater kinetic energy than the other 
forms of matter found on Earth. 

The constant, fast, and random motion of 
gas particles means that they are always colliding 
and thereby transferring kinetic energy back and 
forth without any net loss. These collisions also 
have the overall effect of producing uniform 
pressure in a gas. At the same time, the charac- 
teristics and behavior of gas particles indicate 
that they will tend not to remain in an open con- 
tainer. Therefore, in order to maintain any pres- 
sure on a gas — other than the normal atmos- 
pheric pressure exerted on the surface of the gas 
by the atmosphere (which, of course, is also a 
gas) — it is necessary to keep it in a closed con- 
tainer. 

There are a number of gas laws (examined in 
another essay in this book) describing the 
response of gases to changes in pressure, temper- 
ature, and volume. Among these is Boyle’s law, 
which holds that when the temperature of a gas 
is constant, there is an inverse relationship 
between volume and pressure: in other words, 
the greater the pressure, the less the volume, and 
vice versa. According to a second gas law, 
Charles’s law, for gases in conditions of constant 
pressure, the ratio between volume and tempera- 
ture is constant — that is, the greater the temper- 
ature, the greater the volume, and vice versa. 

In addition, Gay-Lussac’s law shows that the 
pressure of a gas is directly related to its absolute 
temperature on the Kelvin scale: the higher the 
temperature, the higher the pressure, and vice 

VDLUME 2: REAL-LIFE PHYSICS 


versa. Gay-Lussac’s law is combined, along with 
Boyle’s and Charles’s and other gas laws, in the 
ideal gas law, which makes it possible to find the 
value of any one variable — pressure, volume, 
number of moles, or temperature — for a gas, as 
long as one knows the value of the other three. 

□ ther States of Matter 

plasma. Principal among states of 
matter other than solid, liquid, and gas is plasma, 
which is similar to gas. (The term “plasma,” when 
referring to the state of matter, has nothing to do 
with the word as it is often used, in reference to 
blood plasma.) As with gas, plasma particles col- 
lide at high speeds — but in plasma, the speeds are 
even greater, and the kinetic energy levels even 
higher. 

The speed and energy of these collisions is 
directly related to the underlying property that 
distinguishes plasma from gas. So violent are the 
collisions between plasma particles that electrons 
are knocked away from their atoms. As a result, 
plasma does not have the atomic structure typi- 
cal of a gas; rather, it is composed of positive ions 
and electrons. Plasma particles are thus electri- 
cally charged, and, therefore, greatly influenced 
by electrical and magnetic fields. 

Formed at very high temperatures, plasma is 
found in stars and comets’ tails; furthermore, the 
reaction between plasma and atomic particles in 
the upper atmosphere is responsible for the auro- 
ra borealis or “northern lights.” Though not 
found on Earth, plasma — ubiquitous in other 
parts of the universe — may be the most plentiful 
among the four principal states of matter. 

quasi-5 tat e s . Among the quasi- 
states of matter discussed by physicists are sever- 
al terms that describe the structure in which par- 
ticles are joined, rather than the attraction and 
relative movement of those particles. “Crys- 
talline,” “amorphous,” and “glassy” are all terms 
to describe what may be individual states of mat- 
ter; so too is “colloidal.” 

A colloid is a structure intermediate in size 
between a molecule and a visible particle, and it 
has a tendency to be dispersed in another medi- 
um — as smoke, for instance, is dispersed in air. 
Brownian motion describes the behavior of most 
colloidal particles. When one sees dust floating in 
a ray of sunshine through a window, the light 
reflects off colloids in the dust, which are driven 

SCIENCE df everyday things 


back and forth by motion in the air otherwise 
imperceptible to the human senses. 

dark matter. The number of states 
or phases of matter is clearly not fixed, and it is 
quite possible that more will be discovered in 
outer space, if not on Earth. One intriguing can- 
didate is called dark matter, so described because 
it neither reflects nor emits light, and is therefore 
invisible. In fact, luminous or visible matter may 
very well make up only a small fraction of the 
mass in the universe, with the rest being taken up 
by dark matter. 

If dark matter is invisible, how do 
astronomers and physicists know it exists? By 
analyzing the gravitational force exerted on visi- 
ble objects when there seems to be no visible 
object to account for that force. An example is 
the center of our galaxy, the Milky Way, which 
appears to be nothing more than a dark “halo.” In 
order to cause the entire galaxy to revolve around 
it in the same way that planets revolve around the 
Sun, the Milky Way must contain a staggering 
quantity of invisible mass. 

Dark matter may be the substance at the 
heart of a black hole, a collapsed star whose mass 
is so great that its gravitational field prevents 
light from escaping. It is possible, also, that dark 
matter is made up of neutrinos, subatomic parti- 
cles thought to be massless. Perhaps, the theory 
goes, neutrinos actually possess tiny quantities of 
mass, and therefore in huge groups — a mole 
times a mole times a mole — they might possess 
appreciable mass. 

In addition, dark matter may be the deciding 
factor as to whether the universe is infinite. The 
more mass the universe possesses, the greater its 
overall gravity, and if the mass of the universe is 
above a certain point, it will eventually begin to 
contract. This, of course, would mean that it is 
finite; on the other hand, if the mass is below this 
threshold, it will continue to expand indefinitely. 
The known mass of the universe is nowhere near 
that threshold — but, because the nature of dark 
matter is still largely unknown, it is not possible 
yet to say what effect its mass may have on the 
total equation. 

A “NEW” FORM DF MATTER? 

Physicists at the Joint Institute of Laboratory 
Astrophysics in Boulder, Colorado, in 1995 
revealed a highly interesting aspect of atomic 
behavior at temperatures approaching absolute 
zero. Some 70 years before, Einstein had predict- 

SCIENCE DF EVERYDAY THINGS 


ed that, at extremely low temperatures, atoms 
would fuse to form one large “superatom.” This 
hypothesized structure was dubbed the Bose- 
Einstein Condensate (BEC) after Einstein and 
Satyendranath Bose (1894-1974), an Indian 
physicist whose statistical methods contributed 
to the development of quantum theory. 

Cooling about 2,000 atoms of the element 
rubidium to a temperature just 170 billionths of 
a degree Celsius above absolute zero, the physi- 
cists succeeded in creating an atom 100 microm- 
eters across — still incredibly small, but vast in 
comparison to an ordinary atom. The super- 
atom, which lasted for about 15 seconds, cooled 
down all the way to just 20 billionths of a degree 
above absolute zero. The Colorado physicists 
won the Nobel Prize in physics in 1997 for their 
work. 

In 1999, researchers in a lab at Harvard Uni- 
versity also created a superatom of BEC, and 
used it to slow light to just 38 MPH (60.8 
km/h) — about 0.02% of its ordinary speed. 
Dubbed a “new” form of matter, the BEC may 
lead to a greater understanding of quantum 
mechanics, and may aid in the design of smaller, 
more powerful computer chips. 

States and Phases and In 
Between 

At places throughout this essay, references have 
been made variously to “phases” and “states” of 
matter. This is not intended to confuse, but 
rather to emphasize a particular point. Solids, 
liquids, and gases are referred to as “phases,” 
because substances on Earth — water, for 
instance — regularly move from one phase to 
another. This change, a function of temperature, 
is called (aptly enough) “change of phase.” 

There is absolutely nothing incorrect in 
referring to “states of matter.” But “phases of 
matter” is used in the present context as a means 
of emphasizing the fact that most substances, at 
the appropriate temperature and pressure, can be 
solid, liquid, or gas. In fact, a substance may even 
be solid, liquid, and gas. 

An Analogy to Human Life 

The phases of matter can be likened to the phas- 
es of a person’s life: infancy, babyhood, child- 
hood, adolescence, adulthood, old age. The tran- 
sition between these stages is indefinite, yet it is 

VDLUME 2: REAL-LIFE PHYSIGS 


STRUCTURE 
□ F MATTER 


2 1 1 



The response of liquid crystals to light makes them useful in the displays used on laptop comput- 
ers. (AFP/Corbis. Reproduced by permission.) 


| 2 1 Z 


easy enough to say when a person is at a certain 
stage. 

At the transition point between adolescence 
and adulthood — say, at seventeen years old — a 
young person may say that she is an adult, but 
her parents may insist that she is still an adoles- 
cent or a child. And indeed, she might qualify as 
either. On the other hand, when she is thirty, it 
would be ridiculous to assert that she is anything 
other than an adult. 

At the same time, a person at a certain age 
may exhibit behaviors typically associated with 
another age. A child, for instance, may behave 
like an adult, or an adult like a baby. One inter- 
esting example of this is the relationship between 
age two and late adolescence. In both cases, the 
person is in the process of individualizing, devel- 
oping an identity separate from that of his or her 
parents — yet clearly, there are also plenty of dif- 
ferences between a two-year-old and a seventeen- 
year-old. 

As with the transitional phases in human 
life, in the borderline pressure levels and temper- 
atures for phases of matter it is sometimes diffi- 
cult to say, for instance, if a substance is fully a 
liquid or fully a gas. On the other hand, at a cer- 
tain temperature and pressure level, a substance 

VDLUME 2: REAL-LIFE PHYSICS 


clearly is what it is: water at very low temperature 
and pressure, for instance, is indisputably ice — 
just as an average thirty-year-old is obviously an 
adult. As for the second observation, that a per- 
son at one stage in life may reflect characteristics 
of another stage, this too is reflected in the 
behavior of matter. 

liquid crys t a l s . A liquid crystal 
is a substance that, over a specific range of tem- 
perature, displays properties both of a liquid and 
a solid. Below this temperature range, it is 
unquestionably a solid, and above this range it is 
just as obviously a liquid. In between, however, 
liquid crystals exhibit a strange solid-liquid 
behavior: like a liquid, their particles flow, but 
like a solid, their molecules maintain specific 
crystalline arrangements. 

Long, wide, and placed alongside one anoth- 
er, liquid crystal molecules exhibit interesting 
properties in response to light waves. The speed 
of light through a liquid crystal actually varies, 
depending on whether the light is traveling along 
the short or long sides of the molecules. These 
differences in light speed may lead to a change in 
the direction of polarization, or the vibration of 
light waves. 

SCIENCE DF EVERYDAY THINGS 


Structure 
□ f Matter 


KEY TERMS 


atom: The smallest particle of a chem- 

ical element. An atom can exist either alone 
or in combination with other atoms in a 
molecule. Atoms are made up of protons, 
neutrons, and electrons. In most cases, the 
electrical charges in atoms cancel out one 
another; but when an atom loses one or 
more electrons, and thus has a net charge, 
it becomes an ion. 

CHEMICAL COMPOUND: A Sub- 

stance made up of atoms of more than one 
chemical element. These atoms are usually 
joined in molecules. 

chemical element: A substance 

made up of only one kind of atom. 
conservation or energy: A 

law of physics which holds that within a 
system isolated from all other outside fac- 
tors, the total amount of energy remains 
the same, though transformations of ener- 
gy from one form to another take place. 
conservation OF mass: A phys- 

ical principle which states that total mass is 
constant, and is unaffected by factors such 
as position, velocity, or temperature, in any 
system that does not exchange any matter 
with its environment. Unlike the other 
conservation laws, however, conservation 
of mass is not universally applicable, but 
applies only at speeds significant lower 
than that of light — 186,000 mi (297,600 
km) per second. Close to the speed of light, 
mass begins converting to energy. 
conserve: In physics, “to conserve” 

something means “to result in no net loss 
of” that particular component. It is possi- 
ble that within a given system, the compo- 
nent may change form or position, but as 
long as the net value of the component 
remains the same, it has been conserved. 


electron: Negatively charged parti- 

cles in an atom. Electrons, which spin 
around the nucleus of protons and neu- 
trons, constitute a very small portion of the 
atom’s mass. In most atoms, the number of 
electrons and protons is the same, thus 
canceling out one another. When an atom 
loses one or more electrons, however — 
thus becoming an ion — it acquires a net 
electrical charge. 

friction: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

fluid: Any substance, whether gas or 

liquid, that tends to flow, and that con- 
forms to the shape of its container. Unlike 
solids, fluids are typically uniform in 
molecular structure for instance, one mol- 
ecule of water is the same as another water 
molecule. 

□ as: A phase of matter in which mole- 

cules exert little or no attraction toward 
one another, and therefore move at high 
speeds. 

ion: An atom that has lost or gained 

one or more electrons, and thus has a net 
electrical charge. 

liquid: A phase of matter in which 

molecules exert moderate attractions 
toward one another, and therefore move at 
moderate speeds. 

matter: Physical substance that has 

mass; occupies space; is composed of 
atoms; and is ultimately (at speeds 
approaching that of light) convertible to 
energy. There are several phases of matter, 
including solids, liquids, and gases. 


2 1 3 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 



Structure 
□ f Matter 


KEY TERMS continued 


mole: A unit equal to 6.022137 X 10 23 

(more than 600 billion trillion) molecules. 
Their size makes it impossible to weigh 
molecules in relatively small quantities; 
hence the mole facilitates comparisons of 
mass between substances. 

molecule: A group of atoms, usual- 

ly of more than one chemical element, 
joined in a structure. 

neutron: A subatomic particle that 

has no electrical charge. Neutrons are 
found at the nucleus of an atom, alongside 
protons. 

phases of matter: The various 

forms of material substance (matter), 
which are defined primarily in terms of the 
behavior exhibited by their atomic or 
molecular structures. On Earth, three prin- 
cipal phases of matter exist, namely solid, 
liquid, and gas. Other forms of matter 
include plasma. 

plasma: One of the phases of matter, 

closely related to gas. Plasma apparently 


does not exist on Earth, but is found, for 
instance, in stars and comets’ tails. Con- 
taining neither atoms nor molecules, plas- 
ma is made up of electrons and positive 
ions. 

proto n : A positively charged particle 

in an atom. Protons and neutrons, which 
together form the nucleus around which 
electrons orbit, have approximately the 
same mass — a mass that is many times 
greater than that of an electron. 

solid: A phase of matter in which 

molecules exert strong attractions toward 
one another, and therefore move slowly. 

s yste m : In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 
all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 


| 2 1 4 


The cholesteric class of liquid crystals is so 
named because the spiral patterns of light 
through the crystal are similar to those which 
appear in cholesterols. Depending on the physi- 
cal properties of a cholesteric liquid crystal, only 
certain colors may be reflected. The response of 
liquid crystals to light makes them useful in liq- 
uid crystal displays (LCDs) found on laptop 
computer screens, camcorder views, and in other 
applications. 

In some cholesteric liquid crystals, high tem- 
peratures lead to a reflection of shorter visible 
light waves, and lower temperatures to a display 
of longer visible waves. Liquid crystal thermome- 
ters thus show red when cool, and blue as they 
are warmed. This may seem a bit unusual to 
someone who does not understand why the ther- 

vdlume z: real-life physics 


mometer displays those colors, since people typ- 
ically associate red with heat and blue with cold. 

the triple point. A liquid crys- 
tal exhibits aspects of both liquid and solid, and 
thus, at certain temperatures may be classified 
within the crystalline quasi-state of matter. On 
the other hand, the phenomenon known as the 
triple point shows how an ordinary substance, 
such as water or carbon dioxide, can actually be a 
liquid, solid, and vapor — all at once. 

Again, water — the basis of all life on Earth — 
is an unusual substance in many regards. For 
instance, most people associate water as a gas or 
vapor (that is, steam) with very high tempera- 
tures. Yet, at a level far below normal atmospher- 
ic pressure, water can be a vapor at temperatures 
as low as -4°F (-20 °C). (All of the pressure values 

SCIENCE OF EVERYDAY THINGS 



in the discussion of water at or near the triple 
point are far below atmospheric norms: the pres- 
sure at which water would turn into a vapor at - 
4°F, for instance, is about 1/1000 normal atmos- 
pheric pressure.) 

As everyone knows, at relatively low temper- 
atures, water is a solid — ice. But if the pressure of 
ice falls below a very low threshold, it will turn 
straight into a gas (a process known as sublima- 
tion) without passing through the liquid stage. 
On the other hand, by applying enough pressure, 
it is possible to melt ice, and thereby transform it 
from a solid to a liquid, at temperatures below its 
normal freezing point. 

The phases and changes of phase for a given 
substance at specific temperatures and pressure 
levels can be plotted on a graph called a phase 
diagram, which typically shows temperature on 
the x-axis and pressure on the y-axis. The phase 
diagram of water shows a line between the solid 
and liquid states that is almost, but not quite, 
exactly perpendicular to the x-axis: it slopes 
slightly upward to the left, reflecting the fact that 
solid ice turns into water with an increase of 
pressure. 

Whereas the line between solid and liquid 
water is more or less straight, the division 
between these two states and water vapor is 
curved. And where the solid-liquid line intersects 
the vaporization curve, there is a place called the 
triple point. Just below freezing, in conditions 


equivalent to about 0.7% of normal atmospheric 

pressure, water is a solid, liquid, and vapor all at 
once. 

WHERE TD LEARN MORE 

Biel, Timothy L. Atom: Building Blocks of Matter. San 
Diego, CA: Lucent Books, 1990. 

Feynman, Richard. Six Easy Pieces: Essentials of Physics 
Explained by Its Most Brilliant Teacher. New intro- 
duction by Paul Davies. Cambridge, MA: Perseus 
Books, 1995. 

Hewitt, Sally. Solid, Liquid, or Gas? New York: Children’s 
Press, 1998. 

“High School Chemistry Table of Contents — Solids and 
Liquids” Homeworkhelp.com (Web site). <http://www. 
homeworkhelp.com/homeworkhelp/freemember/text 
/chem/hig h/topic09.html> (April 10, 2001). 

“Matter: Solids, Liquids, Gases.” Studyweb (Web site). 
<http://www.studyweb.com/links/4880.html> (April 
10 , 2001 ). 

“The Molecular Circus" (Web site), <http://www.cpo. 
com/Weblabs/circus.html> (April 10, 2001). 

Paul, Richard. A Handbook to the Universe: Explorations 
of Matter, Energy, Space, and Time for Beginning Sci- 
entific Thinkers. Chicago: Chicago Review Press, 

1993. 

“ Phases of Matter” (Web site). <http://pc65.frontier. 
osrhe.edu/hs/science/pphase.html> (April 10, 2001). 

Royston, Angela. Solids, Liquids, and Gasses. Chicago: 
Heinemann Library, 2001. 

Wheeler, Jill C. The Stuff Life’s Made Of: A Book About 
Matter. Minneapolis, MN: Abdo & Daughters Pub- 
lishing, 1996. 


Structure 
□ f Matter 


SCIENCE □ E EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


2 1 5 


THERMODYNAMICS 


I Z 1 6 


C □ N C E PT 

Thermodynamics is the study of the relation- 
ships between heat, work, and energy. Though 
rooted in physics, it has a clear application to 
chemistry, biology, and other sciences: in a sense, 
physical life itself can be described as a con- 
tinual thermodynamic cycle of transformations 
between heat and energy. But these transforma- 
tions are never perfectly efficient, as the second 
law of thermodynamics shows. Nor is it possible 
to get “something for nothing,” as the first law of 
thermodynamics demonstrates: the work output 
of a system can never be greater than the net 
energy input. These laws disappointed hopeful 
industrialists of the early nineteenth century, 
many of whom believed it might be possible to 
create a perpetual motion machine. Yet the laws 
of thermodynamics did make possible such high- 
ly useful creations as the internal combustion 
engine and the refrigerator. 

H □ W IT WDRKS 

Historical Context 

Machines were, by definition, the focal point of 
the Industrial Revolution, which began in Eng- 
land during the late eighteenth and early nine- 
teenth centuries. One of the central preoccupa- 
tions of both scientists and industrialists thus 
became the efficiency of those machines: the 
ratio of output to input. The more output that 
could be produced with a given input, the greater 
the production, and the greater the economic 
advantage to the industrialists and (presumably) 
society as a whole. 

VDLUME 2: REAL-LIFE PHYSICS 


At that time, scientists and captains of 
industry still believed in the possibility of a per- 
petual motion machine: a device that, upon 
receiving an initial input of energy, would con- 
tinue to operate indefinitely without further 
input. As it emerged that work could be convert- 
ed into heat, a form of energy, it began to seem 
possible that heat could be converted directly 
back into work, thus making possible the opera- 
tion of a perfectly reversible perpetual motion 
machine. Unfortunately, the laws of thermody- 
namics dashed all those dreams. 

sndw’s explanation. Some 
texts identify two laws of thermodynamics, while 
others add a third. For these laws, which will be 
discussed in detail below, British writer and sci- 
entist C. R Snow (1905-1980) offered a witty, 
nontechnical explanation. In a 1959 lecture pub- 
lished as The Two Cultures and the Scientific Rev- 
olution, Snow compared the effort to transform 
heat into energy, and energy back into heat again, 
as a sort of game. 

The first law of thermodynamics, in Snow’s 
version, teaches that the game is impossible to 
win. Because energy is conserved, and thus, its 
quantities throughout the universe are always the 
same, one cannot get “something for nothing” by 
extracting more energy than one put into a 
machine. 

The second law, as Snow explained it, offers 
an even more gloomy prognosis: not only is it 
impossible to win in the game of energy-work 
exchanges, one cannot so much as break even. 
Though energy is conserved, that does not mean 
the energy is conserved within the machine 
where it is used: mechanical systems tend toward 
increasing disorder, and therefore, it is impossi- 

SCIENCE □ F EVERYDAY THINGS 




A WOMAN WITH A SUNBURNED NOSE. SUNBURNS ARE CAUSED BY THE SUN'S ULTRAVIOLET RAYS. (Photograph by Lester 
V. Bergman/Corbis. Reproduced by permission.) 


ble for the machine even to return to the original 
level of energy. 

The third law, discovered in 1905, seems to 
offer a possibility of escape from the conditions 
imposed in the second law: at the temperature of 
absolute zero, this tendency toward breakdown 
drops to a level of zero as well. But the third law 
only proves that absolute zero cannot be 
attained: hence, Snow’s third observation, that it 
is impossible to step outside the boundaries of 
this unwinnable heat-energy transformation 
game. 

Wdrk and Energy 

Work and energy, discussed at length elsewhere 
in this volume, are closely related. Work is the 
exertion of force over a given distance to displace 
or move an object. It is thus the product of force 
and distance exerted in the same direction. Ener- 
gy is the ability to accomplish work. 

There are many manifestations of energy, 
including one of principal concern in the present 
context: thermal or heat energy. Other manifes- 
tations include electromagnetic (sometimes 
divided into electrical and magnetic), sound, 
chemical, and nuclear energy. All these, however, 
can be described in terms of mechanical energy, 

SCIENCE □ E EVERYDAY THINGS 


which is the sum of potential energy — the ener- 
gy that an object has due to its position — and 
kinetic energy, or the energy an object possesses 
by virtue of its motion. 

mechanical energy. Kinetic 
energy relates to heat more clearly than does 
potential energy, discussed below; however, it is 
hard to discuss the one without the other. To use 
a simple example — one involving mechanical 
energy in a gravitational field — when a stone is 
held over the edge of a cliff, it has potential ener- 
gy. Its potential energy is equal to its weight 
(mass times the acceleration due to gravity) mul- 
tiplied by its height above the bottom of the 
canyon below. Once it is dropped, it acquires 
kinetic energy, which is the same as one-half its 
mass multiplied by the square of its velocity. 

Just before it hits bottom, the stone’s kinetic 
energy will be at a maximum, and its potential 
energy will be at a minimum. At no point can the 
value of its kinetic energy exceed the value of the 
potential energy it possessed before it fell: the 
mechanical energy, or the sum of kinetic and 
potential energy, will always be the same, though 
the relative values of kinetic and potential energy 
may change. 

VDLUME 2: REAL-LIFE PHYSICS 


2 1 7 



Thermo- 

dynamics 


| 2 1 S 


CONSERVATION CDF ENERGY. 

What mechanical energy does the stone possess 
after it comes to rest at the bottom of the canyon? 
In terms of the system of the stone dropping 
from the cliffside to the bottom, none. Or, to put 
it another way, the stone has just as much 
mechanical energy as it did at the very beginning. 
Before it was picked up and held over the side of 
the cliff, thus giving it potential energy, it was 
presumably sitting on the ground away from the 
edge of the cliff. Therefore, it lacked potential 
energy, inasmuch as it could not be “dropped” 
from the ground. 

If the stone’s mechanical energy — at least in 
relation to the system of height between the cliff 
and the bottom — has dropped to zero, where did 
it go? A number of places. When it hit, the stone 
transferred energy to the ground, manifested as 
heat. It also made a sound when it landed, and 
this also used up some of its energy. The stone 
itself lost energy, but the total energy in the uni- 
verse was unaffected: the energy simply left the 
stone and went to other places. This is an exam- 
ple of the conservation of energy, which is close- 
ly tied to the first law of thermodynamics. 

But does the stone possess any energy at the 
bottom of the canyon? Absolutely. For one thing, 
its mass gives it an energy, known as mass or rest 
energy, that dwarfs the mechanical energy in the 
system of the stone dropping off the cliff. (Mass 
energy is the other major form of energy, aside 
from kinetic and potential, but at speeds well 
below that of light, it is released in quantities that 
are virtually negligible.) The stone may have elec- 
tromagnetic potential energy as well; and of 
course, if someone picks it up again, it will have 
gravitational potential energy. Most important to 
the present discussion, however, is its internal 
kinetic energy, the result of vibration among the 
molecules inside the stone. 

Heat and Temperature 

Thermal energy, or the energy of heat, is really a 
form of kinetic energy between particles at the 
atomic or molecular level: the greater the move- 
ment of these particles, the greater the thermal 
energy. Heat itself is internal thermal energy that 
flows from one body of matter to another. It is 
not the same as the energy contained in a sys- 
tem — that is, the internal thermal energy of the 

VDLUME 2: REAL-LIFE PHYSICS 


system. Rather than being “energy-in-residence,” 
heat is “energy-in-transit.” 

This may be a little hard to comprehend, but 
it can be explained in terms of the stone-and-cliff 
kinetic energy illustration used above. Just as a 
system can have no kinetic energy unless some- 
thing is moving within it, heat exists only when 
energy is being transferred. In the above illustra- 
tion of mechanical energy, when the stone was 
sitting on the ground at the top of the cliff, it was 
analogous to a particle of internal energy in body 
A. When, at the end, it was again on the 
ground — only this time at the bottom of the 
canyon — it was the same as a particle of internal 
energy that has transferred to body B. In 
between, however, as it was falling from one to 
the other, it was equivalent to a unit of heat. 

temperature. In everyday life, peo- 
ple think they know what temperature is: a meas- 
ure of heat and cold. This is wrong for two rea- 
sons: first, as discussed below, there is no such 
thing as “cold” — only an absence of heat. So, 
then, is temperature a measure of heat? Wrong 
again. 

Imagine two objects, one of mass M and the 
other with a mass twice as great, or 2 M. Both 
have a certain temperature, and the question is, 
how much heat will be required to raise their 
temperature by equal amounts? The answer is 
that the object of mass 2 M requires twice as 
much heat to raise its temperature the same 
amount. Therefore, temperature cannot possibly 
be a measure of heat. 

What temperature does indicate is the direc- 
tion of internal energy flow between bodies, and 
the average molecular kinetic energy in transit 
between those bodies. More simply, though a bit 
less precisely, it can be defined as a measure of 
heat differences. (As for the means by which a 
thermometer indicates temperature, that is 
beyond the parameters of the subject at hand; it 
is discussed elsewhere in this volume, in the con- 
text of thermal expansion.) 

MEASURING TEMPERATURE 

and h eat. Temperature, of course, can be 
measured either by the Fahrenheit or Centigrade 
scales familiar in everyday life. Another tempera- 
ture scale of relevance to the present discussion is 
the Kelvin scale, established by William Thom- 
son, Lord Kelvin (1824-1907). 

Drawing on the discovery made by French 
physicist and chemist J. A. C. Charles (1746- 

SCIENCE DF EVERYDAY THINGS 


Thermo- 

dynamics 


1823), that gas at 0°C (32°F) regularly contracts 
by about 1/273 of its volume for every Celsius 
degree drop in temperature, Thomson derived 
the value of absolute zero (discussed below) as 
-273.15°C (-459.67°F). The Kelvin and Celsius 
scales are thus directly related: Celsius tempera- 
tures can be converted to Kelvins (for which nei- 
ther the word nor the symbol for “degree” are 
used) by adding 273.15. 

MEASURING HEAT AND HEAT 

c a pa c i ty. Heat, on the other hand, is meas- 
ured not by degrees (discussed along with the 
thermometer in the context of thermal expan- 
sion), but by the same units as work. Since ener- 
gy is the ability to perform work, heat or work 
units are also units of energy. The principal unit 
of energy in the SI or metric system is the joule 
(J), equal to 1 newton-meter (N • m), and the 
primary unit in the British or English system is 
the foot-pound (ft • lb). One foot-pound is equal 
to 1.356 J, and 1 joule is equal to 0.7376 ft • lb. 

Two other units are frequently used for heat 
as well. In the British system, there is the Btu, or 
British thermal unit, equal to 778 ft • lb. or 1,054 
J. Btus are often used in reference, for instance, to 
the capacity of an air conditioner. An SI unit that 
is also used in the United States — where British 
measures typically still prevail — is the kilocalo- 
rie. This is equal to the heat that must be added 
to or removed from 1 kilogram of water to 
change its temperature by 1°C. As its name sug- 
gests, a kilocalorie is 1,000 calories. A calorie is 
the heat required to change the temperature in 1 
gram of water by 1°C — but the dietary Calorie 
(capital C), with which most people are familiar 
is the same as the kilocalorie. 

A kilocalorie is identical to the heat capacity 
for one kilogram of water. Heat capacity (some- 
times called specific heat capacity or specific 
heat) is the amount of heat that must be added 
to, or removed from, a unit of mass for a given 
substance to change its temperature by 1°C. this 
is measured in units of J/kg • °C (joules per kilo- 
gram-degree Centigrade), though for the sake of 
convenience it is typically rendered in terms of 
kilojoules (1,000 joules): kj/kg • °c. Expressed 
thus, the specific heat of water 4.185 — which is 
fitting, since a kilocalorie is equal to 4.185 kj. 
Water is unique in many aspects, with regard to 
specific heat, in that it requires far more heat to 
raise the temperature of water than that of mer- 
cury or iron. 

SCIENCE DF EVERYDAY THINGS 


REAL-LIFE 
A P P L I C AT I □ N S 

Hdtand “Cold” 

Earlier, it was stated that there is no such thing as 
“cold” — a statement hard to believe for someone 
who happens to be in Buffalo, New York, or 
International Falls, Minnesota, during a Febru- 
ary blizzard. Certainly, cold is real as a sensory 
experience, but in physical terms, cold is not a 
“thing” — it is simply the absence of heat. 

People will say, for instance, that they put an 
ice cube in a cup of coffee to cool it, but in terms 
of physics, this description is backward: what 
actually happens is that heat flows from the cof- 
fee to the ice, thus raising its temperature. The 
resulting temperature is somewhere between that 
of the ice cube and the coffee, but one cannot 
obtain the value simply by averaging the two 
temperatures at the beginning of the transfer. 

For one thing, the volume of the water in the 
ice cube is presumably less than that of the water 
in the coffee, not to mention the fact that their 
differing chemical properties may have some 
minor effect on the interaction. Most important, 
however, is the fact that the coffee did not simply 
merge with the ice: in transferring heat to the ice 
cube, the molecules in the coffee expended some 
of their internal kinetic energy, losing further 
heat in the process. 

cooling machines. Even cool- 
ing machines, such as refrigerators and air condi- 
tioners, actually use heat, simply reversing the 
usual process by which particles are heated. The 
refrigerator pulls heat from its inner compart- 
ment — the area where food and other perish- 
ables are stored — and transfers it to the region 
outside. This is why the back of a refrigerator is 
warm. 

Inside the refrigerator is an evaporator, into 
which heat from the refrigerated compartment 
flows. The evaporator contains a refrigerant — a 
gas, such as ammonia or Freon 12, that readily 
liquifies. This gas is released into a pipe from the 
evaporator at a low pressure, and as a result, it 
evaporates, a process that cools it. The pipe takes 
the refrigerant to the compressor, which pumps 
it into the condenser at a high pressure. Located 
at the back of the refrigerator, the condenser is a 
long series of pipes in which pressure turns the 
gas into liquid. As it moves through the condens- 

VDLUME 2: REAL-LIFE PHYSICS 


2 1 9 


Thermo- 

dynamics 


| zza 


er, the gas heats, and this heat is released into the 
air around the refrigerator. 

An air conditioner works in a similar man- 
ner. Hot air from the room flows into the evapo- 
rator, and a compressor circulates refrigerant 
from the evaporator to a condenser. Behind the 
evaporator is a fan, which draws in hot air from 
the room, and another fan pushes heat from the 
condenser to the outside. As with a refrigerator, 
the back of an air conditioner is hot because it is 
moving heat from the area to be cooled. 

Thus, cooling machines do not defy the 
principles of heat discussed above; nor do they 
defy the laws of thermodynamics that will be dis- 
cussed at the conclusion of this essay. In accor- 
dance with the second law, in order to move heat 
in the reverse of its usual direction, external 
energy is required. Thus, a refrigerator takes in 
energy from a electric power supply (that is, the 
outlet it is plugged into), and extracts heat. 
Nonetheless, it manages to do so efficiently, 
removing two or three times as much heat from 
its inner compartment as the amount of energy 
required to run the refrigerator. 

Transfers of Heat 

It is appropriate now to discuss how heat is trans- 
ferred. One must remember, again, that in order 
for heat to be transferred from one point to 
another, there must be a difference of tempera- 
ture between those two points. If an object or 
system has a uniform level of internal thermal 
energy — no matter how “hot” it may be in ordi- 
nary terms — no heat transfer is taking place. 

Heat is transferred by one of three methods: 
conduction, which involves successive molecular 
collisions; convection, which requires the motion 
of hot fluid from one place to another; or radia- 
tion, which involves electromagnetic waves and 
requires no physical medium for the transfer. 

conduction. Conduction takes 
place best in solids and particularly in metals, 
whose molecules are packed in relatively close 
proximity. Thus, when one end of an iron rod is 
heated, eventually the other end will acquire heat 
due to conduction. Molecules of liquid or non- 
metallic solids vary in their ability to conduct 
heat, but gas — due to the loose attractions 
between its molecules — is a poor conductor. 

When conduction takes place, it is as though 
a long line of people are standing shoulder to 

VDLUME 2: REAL-LIFE PHYSICS 


shoulder, passing a secret down the line. In this 
case, however, the “secret” is kinetic thermal 
energy. And just as the original phrasing of the 
secret will almost inevitably become garbled by 
the time it gets to the tenth or hundredth person, 
some energy is lost in the transfer from molecule 
to molecule. Thus, if one end of the iron rod is 
sitting in a fire and one end is surrounded by air 
at room temperature, it is unlikely that the end in 
the air will ever get as hot as the end in the fire. 

Incidentally, the qualities that make metallic 
solids good conductors of heat also make them 
good conductors of electricity. In the first 
instance, kinetic energy is being passed from 
molecule to molecule, whereas in an electrical 
field, electrons — freed from the atoms of which 
they are normally a part — are able to move along 
the line of molecules. Because plastic is much less 
conductive than metal, an electrician will use 
a screwdriver with a plastic handle. Similarly, 
a metal pan typically has a handle of wood or 
plastic. 

cdnvectidn. There is a term, “con- 
vection oven,” that is actually a redundancy: all 
ovens heat through convection, the principal 
means of transferring heat through a fluid. In 
physics, “fluid” refers both to liquids and gases — 
anything that tends to flow. Instead of simply 
moving heat, as in conduction, convection 
involves the movement of heated material — that 
is, fluid. When air is heated, it displaces cold (that 
is, unheated) air in its path, setting up a convec- 
tion current. 

Convection takes place naturally, as for 
instance when hot air rises from the land on a 
warm day. This heated air has a lower density 
than that of the less heated air in the atmosphere 
above it, and, therefore, is buoyant. As it rises, 
however, it loses energy and cools. This cooled 
air, now more dense than the air around it, sinks 
again, creating a repeating cycle. 

The preceding example illustrates natural 
convection; the heat of an oven, on the other 
hand, is an example of forced convection — a sit- 
uation in which some sort of pump or mecha- 
nism moves heated fluid. So, too, is the cooling 
work of a refrigerator, though the refrigerator 
moves heat in the opposite direction. 

Forced convection can also take place within 
a natural system. The human heart is a pump, 
and blood carries excess heat generated by the 
body to the skin. The heat passes through the 

science df everyday things 


Thermo- 

dynamics 


skin by means of conduction, and at the surface 
of the skin, it is removed from the body in a 
number of ways, primarily by the cooling evapo- 
ration of moisture — that is, perspiration. 

radi at ion. If the Sun is hot — hot 
enough to severely burn the skin of a person who 
spends too much time exposed to its rays — then 
why is it cold in the upper atmosphere? After all, 
the upper atmosphere is closer to the Sun. And 
why is it colder still in the empty space above the 
atmosphere, which is still closer to the Sun? The 
reason is that in outer space there is no medium 
for convection, and in the upper atmosphere, 
where the air molecules are very far apart, there 
is hardly any medium. How, then, does heat 
come to the Earth from the Sun? By radiation, 
which is radically different from conduction or 
convection. The other two involve ordinary ther- 
mal energy, but radiation involves electromag- 
netic energy. 

A great deal of “stuff” travels through the 
electromagnetic spectrum, discussed in another 
essay in this book: radio waves, microwaves for 
television and radar, infrared light, visible light, x 
rays, gamma rays. Though the relatively narrow 
band of visible-light wavelengths is the only part 
of the spectrum of which people are aware in 
everyday life, other parts — particularly the 
infrared and ultraviolet bands — are involved in 
the heat one feels from the Sun. (Ultraviolet rays, 
in fact, cause sunburns.) 

Heat by means of radiation is not as “other- 
worldly” as it might seem: in fact, one does not 
have to point to the Sun for examples of it. Any 
time an object glows as a result of heat — as for 
example, in the case of firelight — that is an 
example of radiation. Some radiation is emitted 
in the form of visible light, but the heat compo- 
nent is in infrared rays. This also occurs in an 
incandescent light bulb. In an incandescent bulb, 
incidentally, much of the energy is lost to the heat 
of infrared rays, and the efficiency of a fluores- 
cent bulb lies in the fact that it converts what 
would otherwise be heat into usable light. 

The Laws of Thermodynamics 

Having explored the behavior of heat, both at the 
molecular level and at levels more easily per- 
ceived by the senses, it is possible to discuss the 
laws of thermodynamics alluded to throughout 
this essay. These laws illustrate the relationships 
between heat and energy examined earlier, and 

SCIENCE DF EVERYDAY THINGS 



Benjamin Thompson, Count Rumford. (Illustration by 
H. Humphrey. UPI/Corbis-Bettmann. Reproduced by permission.) 

show, for instance, why a refrigerator or air con- 
ditioner must have an external source of energy 
to move heat in a direction opposite to its normal 
flow. 

The story of how these laws came to be dis- 
covered is a saga unto itself, involving the contri- 
butions of numerous men in various places over 
a period of more than a century. In 1791, Swiss 
physicist Pierre Prevost (1751-1839) put forth his 
theory of exchanges, stating correctly that all 
bodies radiate heat. Hence, as noted earlier, there 
is no such thing as “cold”: when one holds snow 
in one’s hand, cold does not flow from the snow 
into the hand; rather, heat flows from the hand to 
the snow. 

Seven years later, an American- British physi- 
cist named Benjamin Thompson, Count Rum- 
ford (1753) was boring a cannon with a blunt 
drill when he noticed that this action generated a 
great deal of heat. This led him to question the 
prevailing wisdom, which maintained that heat 
was a fluid form of matter; instead, Thompson 
began to suspect that heat must arise from some 
form of motion. 

carndt’s engine. The next 
major contribution came from the French physi- 
cist and engineer Sadi Carnot (1796-1832). 

VDLUME 2: REAL-LIFE PHYSICS 


22 1 


Thermo- 

dynamics 


| ZZZ 


Though he published only one scientific work, 
Reflections on the Motive Power of Fire (1824), this 
treatise caused a great stir in the European scien- 
tific community. In it, Carnot made the first 
attempt at a scientific definition of work, 
describing it as “weight lifted through a height.” 
Even more important was his proposal for a 
highly efficient steam engine. 

A steam engine, like a modern-day internal 
combustion engine, is an example of a larger 
class of machine called heat engine. A heat 
engine absorbs heat at a high temperature, per- 
forms mechanical work, and, as a result, gives off 
heat a lower temperature. (The reason why that 
temperature must be lower is established in the 
second law of thermodynamics.) 

For its era, the steam engine was what the 
computer is today: representing the cutting edge 
in technology, it was the central preoccupation of 
those interested in finding new ways to accom- 
plish old tasks. Carnot, too, was fascinated by the 
steam engine, and was determined to help over- 
come its disgraceful inefficiency: in operation, a 
steam engine typically lost as much as 95% of its 
heat energy. 

In his Reflections, Carnot proposed that the 
maximum efficiency of any heat engine was 
equal to (T H -T L )/T H , where T H is the highest 
operating temperature of the machine, and T L 
the lowest. In order to maximize this value, T L 
has to be absolute zero, which is impossible to 
reach, as was later illustrated by the third law of 
thermodynamics. 

In attempting to devise a law for a perfectly 
efficient machine, Carnot inadvertently proved 
that such a machine is impossible. Yet his work 
influenced improvements in steam engine 
design, leading to levels of up to 80% efficiency. 
In addition, Carnot’s studies influenced Kelvin — 
who actually coined the term “thermodynam- 
ics” — and others. 

THE FIRST LAW OF THERMO- 
DYNAMICS. During the 1840s, Julius 
Robert Mayer (1814-1878), a German physicist, 
published several papers in which he expounded 
the principles known today as the conservation 
of energy and the first law of thermodynamics. 
As discussed earlier, the conservation of energy 
shows that within a system isolated from all out- 
side factors, the total amount of energy remains 
the same, though transformations of energy 
from one form to another take place. 

VDLUME 2: REAL-LIFE PHYSICS 


The first law of thermodynamics states this 
fact in a somewhat different manner. As with the 
other laws, there is no definitive phrasing; 
instead, there are various versions, all of which 
say the same thing. One way to express the law is 
as follows: Because the amount of energy in a 
system remains constant, it is impossible to per- 
form work that results in an energy output 
greater than the energy input. For a heat engine, 
this means that the work output of the engine, 
combined with its change in internal energy, is 
equal to its heat input. Most heat engines, how- 
ever, operate in a cycle, so there is no net change 
in internal energy. 

Earlier, it was stated that a refrigerator 
extracts two or three times as much heat from its 
inner compartment as the amount of energy 
required to run it. On the surface, this seems to 
contradict the first law: isn’t the refrigerator put- 
ting out more energy than it received? But the 
heat it extracts is only part of the picture, and not 
the most important part from the perspective of 
the first law. 

A regular heat engine, such as a steam or 
internal-combustion engine, pulls heat from a 
high-temperature reservoir to a low-temperature 
reservoir, and, in the process, work is accom- 
plished. Thus, the hot steam from the high-tem- 
perature reservoir makes possible the accom- 
plishment of work, and when the energy is 
extracted from the steam, it condenses in the 
low-temperature reservoir as relatively cool 
water. 

A refrigerator, on the other hand, reverses 
this process, taking heat from a low-temperature 
reservoir (the evaporator inside the cooling com- 
partment) and pumping it to a high-temperature 
reservoir outside the refrigerator. Instead of pro- 
ducing a work output, as a steam engine does, it 
requires a work input — the energy supplied via 
the wall outlet. Of course, a refrigerator does pro- 
duce an “output,” by cooling the food inside, but 
the work it performs in doing so is equal to the 
energy supplied for that purpose. 

THE SECDND LAW OF THER- 
MODYNAMICS. Just a few years after 
Mayer’s exposition of the first law, another Ger- 
man physicist, Rudolph Julius Emanuel Clausius 
(1822-1888) published an early version of the 
second law of thermodynamics. In an 1850 
paper, Clausius stated that “Eleat cannot, of itself, 
pass from a colder to a hotter body.” He refined 

SCIENCE DF EVERYDAY THINGS 


this 15 years later, introducing the concept of 
entropy — the tendency of natural systems 
toward breakdown, and specifically, the tendency 
for the energy in a system to be dissipated. 

The second law of thermodynamics begins 
from the fact that the natural flow of heat is 
always from a high-temperature reservoir to a 
low-temperature reservoir. As a result, no engine 
can be constructed that simply takes heat from a 
source and performs an equivalent amount of 
work: some of the heat will always be lost. In 
other words, it is impossible to build a perfectly 
efficient engine. 

Though its relation to the first law is obvi- 
ous, inasmuch as it further defines the limita- 
tions of machine output, the second law of ther- 
modynamics is not derived from the first. Else- 
where in this volume, the first law of thermody- 
namics — stated as the conservation of energy 
law — is discussed in depth, and, in that context, 
it is in fact necessary to explain how the behavior 
of machines in the real world does not contradict 
the conservation law. 

Even though they mean the same thing, the 
first law of thermodynamics and the conserva- 
tion of energy law are expressed in different ways. 
The first law of thermodynamics states that “the 
glass is half empty,” whereas the conservation of 
energy law shows that “the glass is half full.” The 
thermodynamics law emphasizes the bad news: 
that one can never get more energy out of a 
machine than the energy put into it. Thus, all 
hopes of a perpetual motion machine were 
dashed. The conservation of energy, on the other 
hand, stresses the good news: that energy is never 
lost. 

In this context, the second law of thermody- 
namics delivers another dose of bad news: 
though it is true that energy is never lost, the 
energy available for work output will never be as 
great as the energy put into a system. A car 
engine, for instance, cannot transform all of its 
energy input into usable horsepower; some of the 
energy will be used up in the form of heat and 
sound. Though energy is conserved, usable ener- 
gy is not. 

Indeed, the concept of entropy goes far 
beyond machines as people normally understand 
them. Entropy explains why it is easier to break 
something than to build it — and why, for each 
person, the machine called the human body will 

SCIENCE □ E EVERYDAY THINGS 


inevitably break down and die, or cease to func- 
tion, someday. 

THE THIRD LAW DF THERMO- 
DYNAMICS. The subject of entropy leads 
directly to the third law of thermodynamics, for- 
mulated by German chemist Hermann Walter 
Nernst (1864-1941) in 1905. The third law states 
that at the temperature of absolute zero, entropy 
also approaches zero. From this statement, 
Nernst deduced that absolute zero is therefore 
impossible to reach. 

All matter is in motion at the molecular 
level, which helps define the three major phases 
of matter found on Earth. At one extreme is a 
gas, whose molecules exert little attraction 
toward one another, and are therefore in constant 
motion at a high rate of speed. At the other end 
of the phase continuum (with liquids somewhere 
in the middle) are solids. Because they are close 
together, solid particles move very little, and 
instead of moving in relation to one another, 
they merely vibrate in place. But they do move. 

Absolute zero, or OK on the Kelvin scale of 
temperature, is the point at which all molecular 
motion stops entirely — or at least, it virtually 
stops. (In fact, absolute zero is defined as the 
temperature at which the motion of the average 
atom or molecule is zero.) As stated earlier, 
Carnot’s engine achieves perfect efficiency if its 
lowest temperature is the same as absolute zero; 
but the second law of thermodynamics shows 
that a perfectly efficient machine is impossible. 
This means that absolute zero is an unreachable 
extreme, rather like matter exceeding the speed 
of light, also an impossibility. 

This does not mean that scientists do not 
attempt to come as close as possible to absolute 
zero, and indeed they have come very close. In 
1993, physicists at the Helsinki University of 
Technology Low Temperature Laboratory in Fin- 
land used a nuclear demagnetization device to 
achieve a temperature of 2.8 • Iff 10 K, or 
0.00000000028K. This means that a fragment 
equal to only 28 parts in 100 billion separated 
this temperature from absolute zero — but it was 
still above OK. Such extreme low-temperature 
research has a number of applications, most 
notably with superconductors, materials that 
exhibit virtually no resistance to electrical cur- 
rent at very low temperatures. 

VDLUME 2: REAL-LIFE PHYSICS 


Thermo- 

dynamics 


223 


Thermo- 

dynamics 


| 224 


KEY TERMS 


absolute zero: The temperature, 

defined as OK on the Kelvin scale, at which 
the motion of molecules in a solid virtual- 
ly ceases. The third law of thermodynamics 
establishes the impossibility of actually 
reaching absolute zero. 

BTU (BRITISH THERMAL UNIT): A 

measure of energy or heat in the British 
system, often used in reference to the 
capacity of an air conditioner. A Btu is 
equal to 778 foot-pounds, or 1,054 joules. 
calorie: A measure of heat or energy 

in the SI or metric system, equal to the heat 
that must be added to or removed from 1 
gram of water to change its temperature by 
33.8°F (1°C). The dietary Calorie (capital 
C) with which most people are familiar is 
the same as the kilocalorie. 
conduction: The transfer of heat 

by successive molecular collisions. Con- 
duction is the principal means of heat 
transfer in solids, particularly metals. 

CONSERVATION OF ENERGY: A 

law of physics which holds that within a 
system isolated from all other outside fac- 
tors, the total amount of energy remains 
the same, though transformations of ener- 
gy from one form to another take place. 
The first law of thermodynamics is the 
same as the conservation of energy. 
conserve: In physics, “to conserve” 

something means “to result in no net loss 
of” that particular component. It is possi- 
ble that within a given system, the compo- 
nent may change form or position, but as 
long as the net value of the component 
remains the same, it has been conserved. 
convection: The transfer of heat 

through the motion of hot fluid from one 
place to another. In physics, a “fluid” can be 


either a gas or a liquid, and convection is 
the principal means of heat transfer, for 
instance, in air and water. 
energy: The ability to accomplish 

work. 

entropy: The tendency of natural 

systems toward breakdown, and specifical- 
ly, the tendency for the energy in a system 
to be dissipated. Entropy is closely related 
to the second law of thermodynamics. 

FIRST LAW OF THERMODYNAMICS: 

A law which states the amount of energy in 
a system remains constant, and therefore it 
is impossible to perform work that results 
in an energy output greater than the ener- 
gy input. This is the same as the conserva- 
tion of energy. 

foot-pound: The principal unit of 

energy — and thus of heat — in the British 
or English system. The metric or SI unit is 
the joule. A foot-pound (ft • lb) is equal to 
1.356 J. 

heat: Internal thermal energy that 

flows from one body of matter to another. 
Heat is transferred by three methods con- 
duction, convection, and radiation. 
h eat capac ity: The amount of heat 

that must be added to, or removed from, a 
unit of mass of a given substance to change 
its temperature by 33.8°F (1°C). Heat 
capacity is sometimes called specific heat 
capacity or specific heat. A kilocalorie is 
the heat capacity of 1 gram of water. 
heat engine: A machine that 

absorbs heat at a high temperature, per- 
forms mechanical work, and as a result 
gives off heat at a lower temperature. 
kinetic energy: The energy that 

an object possesses by virtue of its motion. 


VGLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



Thermo- 

dynamics 


KEY TERMS continued 


joule: The principal unit of energy — 

and thus of heat — in the SI or metric sys- 
tem, corresponding to 1 newton-meter (N 
• m). A joule (J) is equal to 0.7376 foot- 
pounds. 

kelvin scale: Established by 

William Thomson, Lord Kelvin (1824- 
1907), the Kelvin scale measures tempera- 
ture in relation to absolute zero, or OK. 
(Units in the Kelvin system, known as 
Kelvins, do not include the word or symbol 
for degree.) The Kelvin and Celsius scales 
are directly related; hence Celsius tempera- 
tures can be converted to Kelvins by adding 
273.15. 

kilocalorie: A measure of heat or 

energy in the SI or metric system, equal to 
the heat that must be added to or removed 
from 1 kilogram of water to change its 
temperature by 33.8°F (1°C). As its name 
suggests, a kilocalorie is 1,000 calories. The 
dietary Calorie (capital C) with which 
most people are familiar is the same as the 
kilocalorie. 

mechanical energy: The sum of 

potential energy and kinetic energy in a 
given system. 

potential energy: The energy 

that an object possesses due to its position. 
radi at i □ n : The transfer of heat by 

means of electromagnetic waves, which 
require no physical medium (e.g., water or 
air) for the transfer. Earth receives the Sun’s 
heat by means of radiation. 

SECDND LAW OF THERMODYNAM- 
ICS: A law of thermodynamics which 

states that no engine can be constructed 
that simply takes heat from a source and 
performs an equivalent amount of work. 
Some of the heat will always be lost, and 


therefore it is impossible to build a perfect- 
ly efficient engine. This is a result of the 
fact that the natural flow of heat is always 
from a high-temperature reservoir to a 
low-temperature reservoir — a fact 

expressed in the concept of entropy. The 
second law is sometimes referred to as “the 
law of entropy.” 

system: In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 
all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 

temperature: The direction of 

internal energy flow between bodies when 
heat is being transferred. Temperature 
measures the average molecular kinetic 
energy in transit between those bodies. 
thermal energy: Heat energy, a 

form of kinetic energy produced by the 
movement of atomic or molecular parti- 
cles. The greater the movement of these 
particles, the greater the thermal energy. 
thermodynamics: The study of 

the relationships between heat, work, and 
energy. 

THIRD LAW DF THERMODYNAMICS: 

A law of thermodynamics which states that 
at the temperature of absolute zero, 
entropy also approaches zero. Zero entropy 
would contradict the second law of ther- 
modynamics, meaning that absolute zero is 
therefore impossible to reach. 
work: The exertion of force over a 

given distance to displace or move an 
object. Work is thus the product of force 
and distance exerted in the same direction. 


225 


SCIENCE OF EVERYDAY THINGS 


VOLUME 2: REAL-LIFE PHYSICS 



WHERE TD LEARN MORE 


THERMO- 

DYNAMICS 


Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Brown, Warren. Alternative Sources of Energy. Introduc- 
tion by Russell E. Train. New York: Chelsea House, 
1994. 

Encyclopedia of Thermodynamics (Web site). 

<http://therion.minpet.unibas.ch/minpet/groups/ 
thermodict/> (April 12, 2001). 

Entropy and the Second Law of Thermodynamics 
(Web site), <http://www.2ndlaw.com> (April 12, 
2001 ). 


Fleisher, Paul. Matter and Energy: Principles of Matter 
and Thermodynamics. Minneapolis, MN: Lerner Pub- 
lications, 2002. 

Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

Moran, Jeffrey B. ELow Do We Know the Laws of Thermo- 
dynamics? New York: Rosen Publishing Group, 2001. 

Santrey, Laurence. Heat. Illustrated by Lloyd Birming- 
ham. Mahwah, N.J.: Troll Associates, 1985. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

“Temperature and Thermodynamics” PhysLLNK.com 
(Web site), <http://www.physlink.com/ae_thermo. 
cfm> (April 12, 2001). 


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VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


H E AT 


C □ N C E PT 

Heat is a form of energy — specifically, the energy 
that flows between two bodies because of differ- 
ences in temperature. Therefore, the scientific 
definition of heat is different from, and more 
precise than, the everyday meaning. Physicists 
working in the area of thermodynamics study 
heat from a number of perspectives, including 
specific heat, or the amount of energy required to 
change the temperature of a substance, and 
calorimetry, the measurement of changes in heat 
as a result of physical or chemical changes. Ther- 
modynamics helps us to understand such phe- 
nomena as the operation of engines and the 
gradual breakdown of complexity in physical sys- 
tems — a phenomenon known as entropy. 

H □ W IT WDRKS 

Heat, Work, and Energy 

Thermodynamics is the study of the relation- 
ships between heat, work, and energy. Work is the 
exertion of force over a given distance to displace 
or move an object, and is, thus, the product of 
force and distance exerted in the same direction. 
Energy, the ability to accomplish work, appears 
in numerous manifestations — including thermal 
energy, or the energy associated with heat. 

Thermal and other types of energy, includ- 
ing electromagnetic, sound, chemical, and 
nuclear energy, can be described in terms of two 
extremes: kinetic energy, or the energy associated 
with movement, and potential energy, or the 
energy associated with position. If a spring is 
pulled back to its maximum point of tension, its 
potential energy is also at a maximum; once it is 
released and begins springing through the air to 

SCIENCE □ F EVERYDAY THINGS 


return to its original position, it begins gaining 
kinetic energy and losing potential energy. 

All manifestations of energy appear in both 
kinetic and potential forms, somewhat like the 
way football teams are organized to play both 
offense or defense. Just as a football team takes an 
offensive role when it has the ball, and a defensive 
role when the other team has it, a physical system 
typically undergoes regular transformations 
between kinetic and potential energy, and may 
have more of one or the other, depending on 
what is taking place in the system. 

What Heat Is and Is Not 

Thermal energy is actually a form of kinetic 
energy generated by the movement of particles at 
the atomic or molecular level: the greater the 
movement of these particles, the greater the ther- 
mal energy. Heat is internal thermal energy that 
flows from one body of matter to another — or, 
more specifically, from a system at a higher tem- 
perature to one at a lower temperature. Thus, 
temperature, like heat, requires a scientific defi- 
nition quite different from its common meaning: 
temperature measures the average molecular 
kinetic energy of a system, and governs the direc- 
tion of internal energy flow between them. 

Two systems at the same temperature are 
said to be in a state of thermal equilibrium. 
When this occurs, there is no exchange of heat. 
Though in common usage, “heat” is an expres- 
sion of relative warmth or coldness, in physical 
terms, heat exists only in transfer between two 
systems. What people really mean by “heat” is the 
internal energy of a system — energy that is a 
property of that system rather than a property of 
transferred internal energy. 

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If you hold a snowball in your hand, as Vanna 
White and her son are doing in this picture, heat 

WILL MOVE FROM YOUR HAND TO THE SNOWBALL. YOUR 
HAND EXPERIENCES THIS AS A SENSATION OF COLD- 
NESS. (Reuters NewMedia Inc./Corbis. Reproduced by permission.) 


ND SUCH THING AS “CHILD.” 

Though the term “cold” has plenty of meaning in 
the everyday world, in physics terminology, it 
does not. Cold and heat are analogous to dark- 
ness and light: again, darkness means something 
in our daily experience, but in physical terms, 
darkness is simply the absence of light. To speak 
of cold or darkness as entities unto themselves is 
rather like saying, after spending 20 dollars, “I 
have 20 non-dollars in my pocket.” 

If you grasp a snowball in your hand, of 
course, your hand gets cold. The human mind 
perceives this as a transfer of cold from the snow- 
ball, but, in fact, exactly the opposite happens: 
heat moves from your hand to the snow, and if 
enough heat enters the snowball, it will melt. At 
the same time, the departure of heat from your 
hand results in a loss of internal energy near the 
surface of your hand, which you experience as a 
sensation of coldness. 

Transfers of Heat 

In holding the snowball, heat passes from the 
surface of the hand by one means, conduction, 
then passes through the snowball by another 


means, convection. In fact, there are three meth- 
ods heat is transferred: conduction, involving 
successive molecular collisions and the transfer 
of heat between two bodies in contact; convec- 
tion, which requires the motion of fluid from one 
place to another; or radiation, which takes place 
through electromagnetic waves and requires no 
physical medium, such as water or air, for the 
transfer. 

conduction. Solids, particularly 
metals, whose molecules are packed relatively 
close together, are the best materials for conduc- 
tion. Molecules of liquid or non-metallic solids 
vary in their ability to conduct heat, but gas is a 
poor conductor, because of the loose attractions 
between its molecules. 

The qualities that make metallic solids good 
conductors of heat, as a matter of fact, also make 
them good conductors of electricity. In the con- 
duction of heat, kinetic energy is passed from 
molecule to molecule, like a long line of people 
standing shoulder to shoulder, passing a secret. 
(And, just as the original phrasing of the secret 
becomes garbled, some kinetic energy is 
inevitably lost in the series of transfers.) 

As for electrical conduction, which takes 
place in a field of electric potential, electrons are 
freed from their atoms; as a result, they are able 
to move along the line of molecules. Because 
plastic is much less conductive than metal, an 
electrician uses a screwdriver with a plastic han- 
dle; similarly, a metal cooking pan typically has a 
wooden or plastic handle. 

cdnvectidn. Wherever fluids are 
involved — and in physics, “fluid” refers both to 
liquids and gases — convection is a common form 
of heat transfer. Convection involves the move- 
ment of heated material — whether it is air, water, 
or some other fluid. 

Convection is of two types: natural convec- 
tion and forced convection, in which a pump or 
other mechanism moves the heated fluid. When 
heated air rises, this is an example of natural con- 
vection. Hot air has a lower density than that of 
the cooler air in the atmosphere above it, and, 
therefore, is buoyant; as it rises, however, it loses 
energy and cools. This cooled air, now denser 
than the air around it, sinks again, creating a 
repeating cycle that generates wind. 

Examples of forced convection include some 
types of ovens and even a refrigerator or air con- 
ditioner. These two machines both move warm 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 


air from an interior to an exterior place. Thus, 
the refrigerator pulls hot air from the compart- 
ment and expels it to the surrounding room, 
while an air conditioner pulls heat from a build- 
ing and releases it to the outside. 

But forced convection does not necessarily 
involve humanmade machines: the human heart 
is a pump, and blood carries excess heat generat- 
ed by the body to the skin. The heat passes 
through the skin by means of conduction, and at 
the surface of the skin, it is removed from the 
body in a number of ways, primarily by the cool- 
ing evaporation of perspiration. 

radi at i d n . Outer space, of course, is 
cold, yet the Sun’s rays warm the Earth, an appar- 
ent paradox. Because there is no atmosphere in 
space, convection is impossible. In fact, heat from 
the Sun is not dependant on any fluid medium 
for its transfer: it comes to Earth by means of 
radiation. This is a form of heat transfer signifi- 
cantly different from the other two, because it 
involves electromagnetic energy, instead of ordi- 
nary thermal energy generated by the action of 
molecules. Heat from the Sun comes through a 
relatively narrow area of the light spectrum, 
including infrared, visible light, and ultra- 
violet rays. 

Every form of matter emits electromagnetic 
waves, though their presence may not be readily 
perceived. Thus, when a metal rod is heated, it 
experiences conduction, but part of its heat is 
radiated, manifested by its glow — visible light. 
Even when the heat in an object is not visible, 
however, it may be radiating electromagnetic 
energy, for instance, in the form of infrared light. 
And, of course, different types of matter radiate 
better than others: in general, the better an object 
is at receiving radiation, the better it is at emit- 
ting it. 

Measuring Heat 

The measurement of temperature by degrees in 
the Fahrenheit or Celsius scales is a part of every- 
day life, but measurements of heat are not as 
familiar to the average person. Because heat is a 
form of energy, and energy is the ability to per- 
form work, heat is, therefore, measured by the 
same units as work. 

The principal unit of work or energy in the 
metric system (known within the scientific com- 
munity as SI, or the SI system) is the joule. 

SCIENCE DF EVERYDAY THINGS 



A REFRIGERATOR IS A TYPE OF REVERSE HEAT ENGINE 
THAT USES A COMPRESSOR, LIKE THE ONE SHOWN AT 
THE BACK OF THIS REFRIGERATOR, TO COOL THE 

refrigerator’s interior. (Ecoscene/Corbis. Reproduced by 
permission.) 

Abbreviated “J,” a joule is equal to 1 newton- 
meter (N • m). The newton is the SI unit of force, 
and since work is equal to force multiplied by 
distance, measures of work can also be separated 
into these components. For instance, the British 
measure of work brings together a unit of dis- 
tance, the foot, and a unit of force, the pound. A 
foot-pound (ft • lb) is equal to 1.356 J, and 1 joule 
is equal to 0.7376 ft • lb. 

In the British system, Btu, or British thermal 
unit, is another measure of energy used for 
machines such as air conditioners. One Btu is 
equal to 778 ft • lb or 1,054 J. The kilocalorie in 
addition to the joule, is an important SI measure 
of heat. The amount of energy required to 
change the temperature of 1 gram of water by 
1°C is called a calorie, and a kilocalorie is equal to 
1,000 calories. Somewhat confusing is the fact 
that the dietary Calorie (capital C), with which 
most people are familiar, is not the same as a 
calorie (lowercase C) — rather, a dietary Calorie is 
the equivalent of a kilocalorie. 

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R E A L- L I F E 
A P P L I C AT I □ N S 

Specific Heat 

Specific heat is the amount of heat that must be 
added to, or removed from, a unit of mass for a 
given substance to change its temperature by 
1°C. Thus, a kilocalorie, because it measures the 
amount of heat necessary to effect that change 
precisely for a kilogram of water, is identical to 
the specific heat for that particular substance in 
that particular unit of mass. 

The higher the specific heat, the more resist- 
ant the substance is to changes in temperature. 
Many metals, in fact, have a low specific heat, 
making them easy to heat up and cool down. 
This contributes to the tendency of metals to 
expand when heated (a phenomenon also dis- 
cussed in the Thermal Expansion essay), and, 
thus, to their malleability. 

MEASURING AND CALCULAT- 
ING specific he at. The specific heat 
of any object is a function of its mass, its compo- 
sition, and the desired change in temperature. 
The values of the initial and final temperature are 
not important — only the difference between 
them, which is the temperature change. 

The components of specific heat are related 
to one another in the formula Q = mc8T. Here Q 
is the quantity of heat, measured in joules, which 
must be added. The mass of the object is desig- 
nated by m, and the specific heat of the particu- 
lar substance in question is represented with c. 
The Greek letter delta (8) designates change, and 
8 T stands for “change in temperature.” 

Specific heat is measured in units of J/kg • °C 
(joules per kilogram-degree Centigrade), though 
for the sake of convenience, this is usually ren- 
dered in terms of kilojoules (kj), or 1,000 
joules — that is, kj/kg • °C. The specific heat of 
water is easily derived from the value of a kilo- 
calorie: it is 4.185, the same number of joules 
required to equal a kilocalorie. 

Calorimetry 

The measurement of heat gain or loss as a result 
of physical or chemical change is called calorime- 
try (pronounced kal-IM-uh-tree). Like the word 
“calorie,” the term is derived from a Latin root 
meaning “heat.” 

VDLUME 2: REAL-LIFE PHYSICS 


The foundations of calorimetry go back to 
the mid-nineteenth century, but the field owes 
much to scientists’ work that took place over a 
period of about 75 years prior to that time. In 
1780, French chemist Antoine Lavoisier (1743- 
1794) and French astronomer and mathemati- 
cian Pierre Simon Laplace (1749-1827) had used 
a rudimentary ice calorimeter for measuring the 
heats in formations of compounds. Around the 
same time, Scottish chemist Joseph Black (1728- 
1799) became the first scientist to make a clear 
distinction between heat and temperature. 

By the mid- 1800s, a number of thinkers had 
come to the realization that — contrary to pre- 
vailing theories of the day — heat was a form of 
energy, not a type of material substance. Among 
these were American-British physicist Benjamin 
Thompson, Count Rumford (1753-1814) and 
English chemist James Joule (1818-1889) — for 
whom, of course, the joule is named. 

Calorimetry as a scientific field of study 
actually had its beginnings with the work of 
French chemist Pierre-Eugene Marcelin Berth- 
elot (1827-1907). During the mid- 1860s, Berth- 
elot became intrigued with the idea of measuring 
heat, and by 1880, he had constructed the first 
real calorimeter. 

calorimeters. Essential to 
calorimetry is the calorimeter, which can be any 
device for accurately measuring the temperature 
of a substance before and after a change occurs. A 
calorimeter can be as simple as a styrofoam cup. 
Its quality as an insulator, which makes styro- 
foam ideal for holding in the warmth of coffee 
and protecting the hand from scalding as well, 
also makes styrofoam an excellent material for 
calorimetric testing. With a styrofoam calorime- 
ter, the temperature of the substance inside the 
cup is measured, a reaction is allowed to take 
place, and afterward, the temperature is meas- 
ured a second time. 

The most common type of calorimeter used 
is the bomb calorimeter, designed to measure the 
heat of combustion. Typically, a bomb calorime- 
ter consists of a large container filled with water, 
into which is placed a smaller container, the com- 
bustion crucible. The crucible is made of metal, 
having thick walls with an opening through 
which oxygen can be introduced. In addition, the 
combustion crucible is designed to be connected 
to a source of electricity. 

SCIENCE DF EVERYDAY THINGS 


In conducting a calorimetric test using a 
bomb calorimeter, the substance or object to be 
studied is placed inside the combustion crucible 
and ignited. The resulting reaction usually occurs 
so quickly that it resembles the explosion of a 
bomb — hence, the name “bomb calorimeter.” 
Once the “bomb” goes off, the resulting transfer 
of heat creates a temperature change in the water, 
which can be readily gauged with a thermometer. 

To study heat changes at temperatures high- 
er than the boiling point of water (212°F or 
100°C), physicists use substances with higher 
boiling points. For experiments involving 
extremely large temperature ranges, an aneroid 
(without liquid) calorimeter may be used. In this 
case, the lining of the combustion crucible must 
be of a metal, such as copper, with a high coeffi- 
cient or factor of thermal conductivity. 

Heat Engines 

The bomb calorimeter that Berthelot designed in 
1880 measured the caloric value of fuels, and was 
applied to determining the thermal efficiency of 
a heat engine. A heat engine is a machine that 
absorbs heat at a high temperature, performs 
mechanical work, and as a result, gives off heat at 
a lower temperature. 

The desire to create efficient heat engines 
spurred scientists to a greater understanding of 
thermodynamics, and this resulted in the laws of 
thermodynamics, discussed at the conclusion of 
this essay. Their efforts were intimately connect- 
ed with one of the greatest heat engines ever cre- 
ated, a machine that literally powered the indus- 
trialized world during the nineteenth century: 
the steam engine. 

HOW A STEAM ENGINE WORKS. 

Like all heat engines (except reverse heat engines 
such as the refrigerator, discussed below), a steam 
engine pulls heat from a high-temperature reser- 
voir to a low-temperature reservoir, and in the 
process, work is accomplished. The hot steam 
from the high-temperature reservoir makes pos- 
sible the accomplishment of work, and when the 
energy is extracted from the steam, the steam 
condenses in the low-temperature reservoir, 
becoming relatively cool water. 

A steam engine is an external-combustion 
engine, as opposed to the internal-combustion 
engine that took its place at the forefront of 
industrial technology at the beginning of the 
twentieth century. Unlike an internal-combus- 

SCIENCE GF EVERYDAY THINGS 


tion engine, a steam engine burns its fuel outside 
the engine. That fuel may be simply firewood, 
which is used to heat water and create steam. The 
thermal energy of the steam is then used to 
power a piston moving inside a cylinder, thus, 
converting thermal energy to mechanical energy 
for purposes such as moving a train. 

EVOLUTION GF STEAM POW- 
ER. As with a number of advanced concepts in 
science and technology, the historical roots of the 
steam engine can be traced to the Greeks, who — 
just as they did with ideas such as the atom or the 
Sun-centered model of the universe — thought 
about it, but failed to develop it. The great inven- 
tor Hero of Alexandria (c. 65- 125) actually creat- 
ed several steam-powered devices, but he per- 
ceived these as mere novelties, hardly worthy of 
scientific attention. Though Europeans adopted 
water power, as, for instance, in waterwheels, 
during the late ancient and medieval periods, 
further progress in steam power did not occur 
for some 1,500 years. 

Following the work of French physicist 
Denis Papin (1647-1712), who invented the pres- 
sure cooker and conducted the first experiments 
with the use of steam to move a piston, English 
engineer Thomas Savery (c. 1650-1715) built the 
first steam engine. Savery had abandoned the use 
of the piston in his machine, but another English 
engineer, Thomas Newcomen (1663-1729), rein- 
troduced the piston for his own steam-engine 
design. 

Then in 1763, a young Scottish engineer 
named James Watt (1736-1819) was repairing a 
Newcomen engine and became convinced he 
could build a more efficient model. His steam 
engine, introduced in 1769, kept the heating and 
cooling processes separate, eliminating the need 
for the engine to pause in order to reheat. These 
and other innovations that followed — including 
the introduction of a high-pressure steam engine 
by English inventor Richard Trevithick (1771- 
1833) — transformed the world. 

CARNOT PROVIDES THEORET- 
ICAL understanding. The men 

who developed the steam engine were mostly 
practical-minded figures who wanted only to 
build a better machine; they were not particular- 
ly concerned with the theoretical explanation for 
its workings. Then in 1824, a French physicist 
and engineer by the name of Sadi Carnot (1796- 
1832) published his sole work, the highly influ- 

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ential Reflections on the Motive Power of Fire 
(1824), in which he discussed heat engines scien- 
tifically. 

In Reflections, Carnot offered the first defini- 
tion of work in terms of physics, describing it as 
“weight lifted through a height.” Analyzing Watt’s 
steam engine, he also conducted groundbreaking 
studies in the nascent science of thermodynam- 
ics. Every heat engine, he explained, has a theo- 
retical limit of efficiency related to the tempera- 
ture difference in the engine: the greater the 
difference between the lowest and highest tem- 
perature, the more efficient the engine. 

Carnot’s work influenced the development 
of more efficient steam engines, and also had an 
impact on the studies of other physicists investi- 
gating the relationship between work, heat, and 
energy. Among these was William Thomson, 
Lord Kelvin (1824-1907). In addition to coining 
the term “thermodynamics,” Kelvin developed 
the Kelvin scale of absolute temperature and 
established the value of absolute zero, equal to 
-273.15°C or -459.67°F. 

According to Carnot’s theory, maximum 
effectiveness was achieved by a machine that 
could reach absolute zero. However, later devel- 
opments in the understanding of thermodynam- 
ics, as discussed below, proved that both maxi- 
mum efficiency and absolute zero are impossible 
to attain. 

REVERSE HE AT ENGINES. It is 

easy to understand that a steam engine is a heat 
engine: after all, it produces heat. But how is it 
that a refrigerator, an air conditioner, and other 
cooling machines are also heat engines? More- 
over, given the fact that cold is the absence of heat 
and heat is energy, one might ask how a refriger- 
ator or air conditioner can possibly use energy to 
produce cold, which is the same as the absence of 
energy. In fact, cooling machines simply reverse 
the usual process by which heat engines operate, 
and for this reason, they are called “reverse heat 
engines.” Furthermore, they use energy to extract 
heat. 

A steam engine takes heat from a high-tem- 
perature reservoir — the place where the water is 
turned into steam — and uses that energy to pro- 
duce work. In the process, energy is lost and the 
heat moves to a low-temperature reservoir, where 
it condenses to form relatively cool water. A 
refrigerator, on the other hand, pulls heat from a 
low-temperature reservoir called the evaporator, 

VDLUME 2: REAL-LIFE PHYSICS 


into which flows heat from the refrigerated com- 
partment — the place where food and other 
perishables are kept. The coolant from the 
evaporator take this heat to the condenser, a 
high-temperature reservoir at the back of the 
refrigerator, and in the process it becomes a gas. 
Heat is released into the surrounding air; this is 
why the back of a refrigerator is hot. 

Instead of producing a work output, as a 
steam engine does, a refrigerator requires a work 
input — the energy supplied via the wall outlet. 
The principles of thermodynamics show that 
heat always flows from a high-temperature to a 
low-temperature reservoir, and reverse heat 
engines do not defy these laws. Rather, they 
require an external power source in order to 
effect the transfer of heat from a low-tempera- 
ture reservoir, through the gases in the evapora- 
tor, to a high-temperature reservoir. 

The Laws of Thermodynamics 


THE FIRST LAW DF THERMO- 
DYNAMICS. There are three laws of ther- 
modynamics, which provide parameters as to the 
operation of thermal systems in general, and heat 
engines in particular. The history behind the der- 
ivation of these laws is discussed in the essay on 
Thermodynamics; here, the laws themselves will 
be examined in brief form. 

The physical law known as conservation of 
energy shows that within a system isolated from 
all outside factors, the total amount of energy 
remains the same, though transformations of 
energy from one form to another take place. The 
first law of thermodynamics states the same fact 
in a somewhat different manner. 

According to the first law of thermodynam- 
ics, because the amount of energy in a system 
remains constant, it is impossible to perform 
work that results in an energy output greater 
than the energy input. Thus, it could be said that 
the conservation of energy law shows that “the 
glass is half full”: energy is never lost. On the 
hand, the first law of thermodynamics shows that 
“the glass is half empty”: no machine can ever 
produce more energy than was put into it. Hence, 
a perpetual motion machine is impossible, 
because in order to keep a machine running 
continually, there must be a continual input of 
energy. 

THE SECOND LAW DF THER- 
MODYNAMICS. The second law of ther- 

SCIENCE OF EVERYDAY THINGS 


H EAT 


KEY TERMS 


absolute zero: The temperature, 

defined as OK on the Kelvin scale, at which 
the motion of molecules in a solid virtual- 
ly ceases. The third law of thermodynamics 
establishes the impossibility of actually 
reaching absolute zero. 

BTU (BRITISH THERMAL UNIT): A 

measure of energy or heat in the British 
system, often used in reference to the 
capacity of an air conditioner. A Btu is 
equal to 778 foot-pounds, or 1,054 joules. 

calorie: A measure of heat or energy 

in the SI or metric system, equal to the heat 
that must be added to or removed from 1 
gram of water to change its temperature by 
1°C. The dietary Calorie (capital C) with 
which most people are familiar is the same 
as the kilocalorie. 

caldrimetry: The measurement of 

heat gain or loss as a result of physical or 
chemical change. 

conduction: The transfer of heat 

by successive molecular collisions. Con- 
duction is the principal means of heat 
transfer in solids, particularly metals. 

CONSERVATION OF ENERGY: A 

law of physics stating that within a system 
isolated from all other outside factors, the 
total amount of energy remains the same, 
though transformations of energy from 
one form to another take place. The first 
law of thermodynamics is the same as the 
conservation of energy. 
convection: The transfer of heat 

through the motion of hot fluid from one 
place to another. In physics, a “fluid” can be 


either a gas or a liquid, and convection is 
the principal means of heat transfer, for 
instance, in air and water. 

energy: The ability to accomplish 

work. 

entropy: The tendency of natural 

systems toward breakdown, and specifical- 
ly, the tendency for the energy in a system 
to be dissipated. Entropy is closely related 
to the second law of thermodynamics. 

FIRST LAW OF THERMODYNAMICS: 

A law stating that the amount of energy in 
a system remains constant, and therefore, it 
is impossible to perform work that results 
in an energy, output greater than the ener- 
gy input. This is the same as the conserva- 
tion of energy. 

foot-pound: The principal unit of 

energy — and, thus, of heat — in the British 
or English system. The metric or SI unit is 
the joule. A foot-pound (ft • lb) is equal to 
1.356 J. 

heat: Internal thermal energy that 

flows from one body of matter to another. 
Heat is transferred by three methods con- 
duction, convection, and radiation. 

heat engine: A machine that 

absorbs heat at a high temperature, per- 
forms mechanical work, and, as a result, 
gives off heat at a lower temperature. 

joule: The principal unit of energy — 

and, thus, of heat — in the SI or metric sys- 
tem, corresponding to 1 newton-meter 
(N • m). A joule (J) is equal to 0.7376 foot- 
pounds. 


233 


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VOLUME 2: REAL-LIFE PHYSICS 



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KEY TERMS continued 


kelvin scale: Established by 

William Thomson, Lord Kelvin (1824- 
1907), the Kelvin scale measures tempera- 
ture in relation to absolute zero, or OK. 
(Units in the Kelvin system, known as 
Kelvins, do not include the word or symbol 
for degree.) The Kelvin and Celsius scales 
are directly related; hence, Celsius temper- 
atures can be converted to Kelvins by 
adding 273.15. 

kilocalorie: A measure of heat or 

energy in the SI or metric system, equal to 
the heat that must be added to or removed 
from 1 kilogram of water to change its 
temperature by 1°C. As its name suggests, a 
kilocalorie is 1,000 calories. The dietary 
Calorie (capital C) with which most people 
are familiar, is the same as the kilocalorie. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 


potential energy: The energy 

that an object possesses due to its position. 

radiation: The transfer of heat by 

means of electromagnetic waves, which 
require no physical medium (for example, 
water or air) for the transfer. Earth receives 
the Sun’s heat by means of radiation. 

SECOND LAW OF THERMODYNAM- 
ICS: A law of thermodynamics stating 

that no engine can be constructed that 
simply takes heat from a source and per- 
forms an equivalent amount of work. 
Some of the heat will always be lost, and, 
therefore, it is impossible to build a 
perfectly efficient engine. This is a result of 
the fact that the natural flow of heat is 
always from a high-temperature reservoir 
to a low-temperature reservoir — a fact 
expressed in the concept of entropy. The 
second law is sometimes referred to as “the 
law of entropy.” 


| 234 


modynamics begins from the fact that the natu- 
ral flow of heat is always from a high-tempera- 
ture to a low-temperature reservoir. As a result, 
no engine can be constructed that simply takes 
heat from a source and performs an equivalent 
amount of work: some of the heat will always be 
lost. In other words, it is impossible to build a 
perfectly efficient engine. 

In effect, the second law of thermodynamics 
compounds the “bad news” delivered by the first 
law with some even worse news: though it is true 
that energy is never lost, the energy available for 
work output will never be as great as the energy 
put into a system. Linked to the second law is the 
concept of entropy, the tendency of natural sys- 
tems toward breakdown, and specifically, the ten- 
dency for the energy in a system to be dissipated. 
“Dissipated” in this context means that the high- 
and low-temperature reservoirs approach equal 

VDLUME 2: REAL-LIFE PHYSICS 


temperatures, and as this occurs, entropy 
increases. 

THE THIRD LAW OF THERMO- 
DYNAMICS. Entropy also plays a part in the 
third law of thermodynamics, which states that at 
the temperature of absolute zero, entropy also 
approaches zero. This might seem to counteract 
the “worse news” of the second law, but in fact, 
what the third law shows is that absolute zero is 
impossible to reach. 

As stated earlier, Carnot’s engine would 
achieve perfect efficiency if its lowest tempera- 
ture were the same as absolute zero; but the sec- 
ond law of thermodynamics shows that a per- 
fectly efficient machine is impossible. Relativity 
theory (which first appeared in 1905, the same 
year as the third law of thermodynamics) showed 
that matter can never exceed the speed of light. 
In the same way, the collective effect of the sec- 
ond and third laws is to prove that absolute 

SCIENCE DF EVERYDAY THINGS 



H EAT 


KEY TERMS continued 


specific heat: The amount of heat 

that must be added to, or removed from, a 
unit of mass of a given substance to change 
its temperature by 1°C. A kilocalorie is the 
specific heat of 1 gram of water. 

s yste m : In physics, the term “system” 

usually refers to any set of physical interac- 
tions isolated from the rest of the universe. 
Anything outside of the system, including 
all factors and forces irrelevant to a discus- 
sion of that system, is known as the envi- 
ronment. 

temperature: The direction of 

internal energy flow between two systems 
when heat is being transferred. Tempera- 
ture measures the average molecular kinet- 
ic energy in transit between those systems. 

thermal energy: Heat energy, a 

form of kinetic energy produced by the 
movement of atomic or molecular parti- 


cles. The greater the movement of these 
particles, the greater the thermal energy. 

THERMAL EQUILIBRIUM: The State 

that exists when two systems have the same 
temperature. As a result, there is no 
exchange of heat between them. 

thermodynamics: The study of 

the relationships between heat, work, and 
energy. 

THIRD LAW DF THERMODYNAMICS: 

A law of thermodynamics which states that 
at the temperature of absolute zero, 
entropy also approaches zero. Zero entropy 
would contradict the second law of ther- 
modynamics, meaning that absolute zero 
is, therefore, impossible to reach. 

work: The exertion of force over a 

given distance to displace or move an 
object. Work is, thus, the product of force 
and distance exerted in the same direction. 


zero — the temperature at which molecular 
motion in all forms of matter theoretically ceas- 
es — can never be reached. 

WHERE TO LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

Bonnet, Robert L and Dan Keen. Science Fair Projects: 
Physics. Illustrated by Frances Zweifel. New York: 
Sterling, 1999. 

Encyclopedia of Thermodynamics (Web site). <http:// 
therion.minpet.unibas.ch/minpet/groups/ 
thermodict/> (April 12, 2001). 

Friedhoffer, Robert. Physics Lab in the Home. Illustrated 
by Joe Hosking. New York: Franklin Watts, 1997. 


Manning, Mick and Brita Granstrom. Science School. 
New York: Kingfisher, 1998. 

Macaulay, David. The New Way Things Work. Boston: 
Houghton Mifflin, 1998. 

Moran, Jeffrey B. How Do We Know the Laws of Thermo- 
dynamics? New York: Rosen Publishing Group, 2001. 

Santrey, Laurence. Heat. Illustrated by Lloyd Birming- 
ham. Mahwah, NJ: Troll Associates, 1985. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

“Temperature and Thermodynamics” PhysLLNK.com 
(Web site), <http://www.physlink.com/ae_ 
thermo.cfm> (April 12, 2001). 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


235 



TEMPER AT U R E 


| Z36 


C □ N C E PT 

Temperature is one of those aspects of the every- 
day world that seems rather abstract when 
viewed from the standpoint of physics. In scien- 
tific terms, it is not simply a measure of hot and 
cold, but an indicator of molecular motion and 
energy flow. Thermometers measure tempera- 
ture by a number of means, including the expan- 
sion that takes place in a medium such as mercu- 
ry or alcohol. These measuring devices are 
gauged in several different ways, with scales 
based on the freezing and boiling points of 
water — as well as, in the case of the absolute 
temperature scale, the point at which all molecu- 
lar motion virtually ceases. 

H □ W IT WDRKS 

Heat 

Energy appears in many forms, including ther- 
mal energy, or the energy associated with heat. 
Heat is internal thermal energy that flows from 
one body of matter to another — or, more specif- 
ically, from a system at a higher temperature to 
one at a lower temperature. 

Two systems at the same temperature are 
said to be in a state of thermal equilibrium. 
When this occurs, there is no exchange of heat. 
Though people ordinarily speak of “heat” as an 
expression of relative warmth or coldness, in 
physical terms, heat only exists in transfer 
between two systems. It is never something 
inherently part of a system; thus, unless there is a 
transfer of internal energy, there is no heat, sci- 
entifically speaking. 

VOLUME 2: REAL-LIFE PHYSICS 


HEAT: ENERGY IN TRANSIT. 

Thus, heat cannot be said to exist unless there is 
one system in contact with another system of dif- 
fering temperature. This can be illustrated by way 
of the old philosophical question: “If a tree falls 
in the woods when there is no one to hear it, does 
it make a sound?” From a physicist’s point of 
view, of course, sound waves are emitted whether 
or not there is an ear to receive their vibrations; 
but, consider this same scenario in terms of heat. 
First, replace the falling tree with a hypothetical 
object possessing a certain amount of internal 
energy; then replace sound waves with heat. In 
this case, if this object is not in contact with 
something else that has a different temperature, 
it “does not make a sound” — in other words, it 
transfers no internal energy, and, thus, there is no 
heat from the standpoint of physics. 

This could even be true of two incredibly 
“hot” objects placed next to one another inside a 
vacuum — an area devoid of matter, including air. 
If both have the same temperature, there is no 
heat, only two objects with high levels of internal 
energy. Note that a vacuum was specified: assum- 
ing there was air around them, and that the air 
was of a lower temperature, both objects would 
then be transferring heat to the air. 

RELATIVE MOTION BETWEEN 

molecules. If heat is internal thermal 
energy in transfer, from whence does this energy 
originate? From the movement of molecules. 
Every type of matter is composed of molecules, 
and those molecules are in motion relative to one 
another. The greater the amount of relative 
motion between molecules, the greater the kinet- 
ic energy, or the energy of movement, which is 
manifested as thermal energy. Thus, “heat” — to 

science of everyday things 



use the everyday term for what physicists 
describe as thermal energy — is really nothing 
more than the result of relative molecular 
motion. Thus, thermal energy is sometimes iden- 
tified as molecular translational energy. 

Note that the molecules are in relative 
motion, meaning that if one were “standing” on 
a molecule, one would see the other molecules 
moving. This is not the same as movement on the 
part of a large object composed of molecules; in 
this case, molecules themselves are not directly 
involved in relative motion. 

Put another way, the movement of Earth 
through space is an entirely different type of 
movement from the relative motion of objects on 
Earth — people, animals, natural forms such as 
clouds, manmade forms of transportation, and 
so forth. In this example, Earth is analogous to a 
“large” item of matter, such as a baseball, a 
stream of water, or a cloud of gas. 

The smaller objects on Earth are analogous 
to molecules, and, in both cases, the motion of 
the larger object has little direct impact on the 
motion of smaller objects. Hence, as discussed in 
the Frame of Reference essay, it is impossible to 
perceive with one’s senses the fact that Earth is 
actually hurling through space at incredible 
speeds. 

MOLECULAR MOTION AND 

phases of m att e r . The relative 
motion of molecules determines phase of mat- 
ter — that is, whether something is a solid, liquid, 
or gas. When molecules move quickly in relation 
to one another, they exert a small electromagnet- 
ic attraction toward one another, and the larger 
material of which they are a part is called a gas. A 
liquid, on the other hand, is a type of matter in 
which molecules move at moderate speeds in 
relation to one another, and therefore exert a 
moderate intermolecular attraction. 

The kinetic theory of gases relates molecular 
motion to energy in gaseous substances. It does 
not work as well in relation to liquids and solids; 
nonetheless, it is safe to say that — generally 
speaking — a gas has more energy than a liquid, 
and a liquid more energy than a solid. In a solid, 
the molecules undergo very little relative motion: 
instead of bumping into each other, like gas mol- 
ecules and (to a lesser extent) liquid molecules, 
solid molecules merely vibrate in place. 

SCIENCE df everyday things 



William Thomson, (better known as Lord Kelvin) 

ESTABLISHED WHAT IS NOW KNOWN AS THE KELVIN 
SCALE. 

Understanding Temperature 

As with heat, temperature requires a scientific 
definition quite different from its common 
meaning. Temperature may be defined as a meas- 
ure of the average molecular translational energy 
in a system — that is, in any material body. 

Because it is an average, the mass or other 
characteristics of the body do not matter. A large 
quantity of one substance, because it has more 
molecules, possesses more thermal energy than a 
smaller quantity of that same substance. Since it 
has more thermal energy, it transfers more heat 
to any body or system with which it is in contact. 
Yet, assuming that the substance is exactly the 
same, the temperature, as a measure of average 
energy, will be the same as well. 

Temperature determines the direction of 
internal energy flow between two systems when 
heat is being transferred. This can be illustrated 
through an experience familiar to everyone: hav- 
ing one’s temperature taken with a thermometer. 
If one has a fever, one’s mouth will be warmer 
than the thermometer, and therefore heat will be 
transferred to the thermometer from the mouth 
until the two objects have the same temperature. 

VDLUME 2: REAL-LIFE PHYSICS 


Temperature 


23 V 


Temperature 


| 2 3 S 



A THERMOMETER WORKS BY MEASURING THE LEVEL OF 
THERMAL EXPANSION EXPERIENCED BY A MATERIAL 
WITHIN THE THERMOMETER. MERCURY HAS BEEN A COM- 
MON THERMOMETER MATERIAL SINCE THE 1 VDDS. (Pi 10 - 

tograph by Michael Prince/Corbis. Reproduced by permission.) 

At that point of thermal equilibrium, a tempera- 
ture reading can be taken from the thermometer. 

TEMPERATURE AND HEAT 

fldw. The principles of thermodynamics — 
the study of the relationships between heat, 
work, and energy, show that heat always flows 
from an area of higher temperature to an area of 
lower temperature. The opposite simply cannot 
happen, because coldness, though it is very real 
in terms of sensory experience, is not an inde- 
pendent phenomenon. There is not, strictly 
speaking, such a thing as “cold” — only the 
absence of heat, which produces the sensation of 
coldness. 

One might pour a kettle of boiling water 
into a cold bathtub to heat it up; or put an ice 
cube in a hot cup of coffee “to cool it down.” 
These seem like two very different events, but 
from the standpoint of thermodynamics, they 
are exactly the same. In both cases, a body of high 
temperature is placed in contact with a body of 
low temperature, and in both cases, heat passes 
from the high-temperature body to the low-tem- 
perature one. 


The boiling water warms the tub of cool 
water, and due to the high ratio of cool water to 
boiling water in the bathtub, the boiling water 
expends all its energy raising the temperature in 
the bathtub as a whole. The greater the ratio of 
very hot water to cool water, on the other hand, 
the warmer the bathtub will be in the end. But 
even after the bath water is heated, it will contin- 
ue to lose heat, assuming the air in the room is 
not warmer than the water in the tub. If the water 
in the tub is warmer than the air, it immediately 
begins transferring thermal energy to the low- 
temperature air until their temperatures are 
equalized. 

As for the coffee and the ice cube, what hap- 
pens is quite different from, indeed, opposite to, 
the common understanding of the process. In 
other words, the ice does not “cool down” the 
coffee: the coffee warms up the ice and presum- 
ably melts it. Once again, however, it expends at 
least some of its thermal energy in doing so, and 
as a result, the coffee becomes cooler than it was. 

If the coffee is placed inside a freezer, there is 
a large temperature difference between it and the 
surrounding environment — so much so that if it 
is left for hours, the once-hot coffee will freeze. 
But again, the freezer does not cool down the cof- 
fee; the molecules in the coffee respond to the 
temperature difference by working to warm up 
the freezer. In this case, they have to “work over- 
time,” and since the freezer has a constant supply 
of electrical energy, the heated molecules of the 
coffee continue to expend themselves in a futile 
effort to warm the freezer. Eventually, the coffee 
loses so much energy that it is frozen solid; 
meanwhile, the heat from the coffee has been 
transferred outside the freezer to the atmosphere 
in the surrounding room. 

THERMAL EXPANSION AND 

equilibrium. Temperature is related to 
the concept of thermal equilibrium, and has an 
effect on thermal expansion. As discussed below, 
as well as within the context of thermal expan- 
sion, a thermometer provides a gauge of temper- 
ature by measuring the level of thermal expan- 
sion experienced by a material (for example, 
mercury) within the thermometer. 

In the examples used earlier — the ther- 
mometer in the mouth, the hot water in the cool 
bathtub, and the ice cube in the cup of coffee — 
the systems in question eventually reach thermal 
equilibrium. This is rather like averaging their 
temperatures, though, in fact, the equation 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 



involved is more complicated than a simple 
arithmetic average. 

In the case of an ordinary mercury ther- 
mometer, the need to achieve thermal equilibri- 
um explains why one cannot get an instanta- 
neous temperature reading: first, the mouth 
transfers heat to the thermometer, and once both 
mouth and thermometer reach the same temper- 
ature, they are in thermal equilibrium. At that 
point, it is possible to gauge the temperature of 
the mouth by reading the thermometer. 

REAL-LIFE 
A P P L I C AT I □ N S 

Development of the Ther- 
mometer 

A thermometer can be defined scientifically as a 
device that gauges temperature by measuring a 
temperature-dependent property, such as the 
expansion of a liquid in a sealed tube. As with 
many aspects of scientific or technological 
knowledge, the idea of the thermometer 
appeared in ancient times, but was never devel- 
oped. Again, like so many other intellectual phe- 
nomena, it lay dormant during the medieval 
period, only to be resurrected at the beginning of 
the modern era. 

The Greco-Roman physician Galen (c. 129- 
216) was among the first thinkers to envision a 
scale for measuring temperature. Of course, what 
he conceived of as “temperature” was closer to 
the everyday meaning of that term, not its more 
precise scientific definition: the ideas of molecu- 
lar motion, heat, and temperature discussed in 
this essay emerged only in the period beginning 
about 1750. In any case, Galen proposed that 
equal amounts of boiling water and ice be com- 
bined to establish a “neutral” temperature, with 
four units of warmth above it and four degrees of 
cold below. 

the thermdscdpe. The great 
physicist Galileo Galilei (1564-1642) is some- 
times credited with creating the first practical 
temperature measuring device, called a thermo- 
scope. Certainly Galileo — whether or not he was 
the first — did build a thermoscope, which con- 
sisted of a long glass tube planted in a container 
of liquid. Prior to inserting the tube into the liq- 
uid — which was usually colored water, though 
Galileo’s thermoscope used wine — as much air as 

SCIENCE □ F EVERYDAY THINGS 


possible was removed from the tube. This creat- 
ed a vacuum, and as a result of pressure differ- 
ences between the liquid and the interior of the 
thermoscope tube, some of the liquid went into 
the tube. 

But the liquid was not the thermometric 
medium — that is, the substance whose tempera- 
ture-dependent property changes the thermo- 
scope measured. (Mercury, for instance, is the 
thermometric medium in most thermometers 
today.) Instead, the air was the medium whose 
changes the thermoscope measured: when it was 
warm, the air expanded, pushing down on the 
liquid; and when the air cooled, it contracted, 
allowing the liquid to rise. 

It is interesting to note the similarity in 
design between the thermoscope and the barom- 
eter, a device for measuring atmospheric pressure 
invented by Italian physicist Evangelista Torricel- 
li (1608-1647) around the same time. Neither 
were sealed, but by the mid-seventeenth century, 
scientists had begun using sealed tubes contain- 
ing liquid instead of air. These were the first true 
thermometers. 

early thermometers. Ferdi- 
nand II, Grand Duke of Tuscany (1610-1670), is 
credited with developing the first thermometer 
in 1641. Ferdinand’s thermometer used alcohol 
sealed in glass, which was marked with a temper- 
ature scale containing 50 units. It did not, how- 
ever, designate a value for zero. 

English physicist Robert Elooke (1635-1703) 
created a thermometer using alcohol dyed red. 
Hooke’s scale was divided into units equal to 
about 1/500 of the volume of the thermometric 
medium, and for the zero point, he chose the 
temperature at which water freezes. Thus, Hooke 
established a standard still used today; likewise, 
his thermometer itself set a standard. Built in 
1664, it remained in use by the Royal Society — 
the foremost organization for the advancement 
of science in England during the early modern 
period — until 1709. 

Olaus Roemer (1644-1710), a Danish 
astronomer, introduced another important stan- 
dard. In 1702, he built a thermometer based not 
on one but two fixed points, which he designated 
as the temperature of snow or crushed ice, and 
the boiling point of water. As with Hooke’s use of 
the freezing point, Roemer’s idea of the freezing 
and boiling points of water as the two parameters 

VDLUME 2: REAL-LIFE PHYSICS 


Temperature 


239 


Temperature 


| 24D 


for temperature measurements has remained in 
use ever since. 

Temperature Scales 

fa h r e n h e i t. Not only did he devel- 
op the Fahrenheit scale, oldest of the temperature 
scales still used in Western nations today, but 
German physicist Daniel Fahrenheit (1686-1736) 
also built the first thermometer to contain mer- 
cury as a thermometric medium. Alcohol has a 
low boiling point, whereas mercury remains fluid 
at a wide range of temperatures. In addition, it 
expands and contracts at a very constant rate, 
and tends not to stick to glass. Furthermore, its 
silvery color makes a mercury thermometer easy 
to read. 

Fahrenheit also conceived the idea of using 
“degrees” to measure temperature in his ther- 
mometer, which he introduced in 1714. It is no 
mistake that the same word refers to portions of 
a circle, or that exactly 180 degrees — half the 
number in a circle — separate the freezing and 
boiling points for water on Fahrenheit’s ther- 
mometer. Ancient astronomers attempting to 
denote movement in the skies used a circle with 
360 degrees as a close approximation of the ratio 
between days and years. The number 360 is also 
useful for computations, because it has a large 
quantity of divisors, as does 180 — a total of 16 
whole-number divisors other than 1 and itself. 

Though it might seem obvious that 0 should 
denote the freezing point and 180 the boiling 
point on Fahrenheit’s scale, such an idea was far 
from obvious in the early eighteenth century. 
Fahrenheit considered the idea not only of a 0- 
to-180 scale, but also of a 180-to-360 scale. In the 
end, he chose neither — or rather, he chose not to 
equate the freezing point of water with zero on 
his scale. For zero, he chose the coldest possible 
temperature he could create in his laboratory, 
using what he described as “a mixture of sal 
ammoniac or sea salt, ice, and water.” Salt lowers 
the melting point of ice (which is why it is used 
in the northern United States to melt snow and 
ice from the streets on cold winter days), and, 
thus, the mixture of salt and ice produced an 
extremely cold liquid water whose temperature 
he equated to zero. 

With Fahrenheit’s scale, the ordinary freez- 
ing point of water was established at 32°, and the 
boiling point exactly 180° above it, at 212°. Just a 
few years after he introduced his scale, in 1730, a 

VDLUME 2: REAL-LIFE PHYSICS 


French naturalist and physicist named Rene 
Antoine Ferchault de Reaumur (1683-1757) pre- 
sented a scale for which 0° represented the freez- 
ing point of water and 80° the boiling point. 
Although the Reaumur scale never caught on to 
the same extent as Fahrenheit’s, it did include one 
valuable addition: the specification that temper- 
ature values be determined at standard sea-level 
atmospheric pressure. 

Celsius. With its 32-degree freezing 
point and its 212-degree boiling point, the 
Fahrenheit system is rather ungainly, lacking the 
neat orderliness of a decimal or base- 10 scale. 
The latter quality became particularly important 
when, 10 years after the French Revolution of 
1789, France adopted the metric system for 
measuring length, mass, and other physical phe- 
nomena. The metric system eventually spread to 
virtually the entire world, with the exception of 
English-speaking countries, where the more 
cumbersome British system still prevails. But 
even in the United States and Great Britain, sci- 
entists use the metric system. The metric temper- 
ature measure is the Celsius scale, created in 1742 
by Swedish astronomer Anders Celsius (1701- 
1744). 

Like Fahrenheit, Celsius chose the freezing 
and boiling points of water as his two reference 
points, but he determined to set them 100, rather 
than 180, degrees apart. Interestingly, he planned 
to equate 0° with the boiling point, and 100° with 
the freezing point — proving that even the most 
apparently obvious aspects of a temperature scale 
were once open to question. Only in 1750 did fel- 
low Swedish physicist Martin Stromer change the 
orientation of the Celsius scale. 

Celsius’s scale was based not simply on the 
boiling and freezing points of water, but, specifi- 
cally, those points at normal sea-level atmospher- 
ic pressure. The latter, itself a unit of measure 
known as an atmosphere (atm), is equal to 14.7 
lb/in 2 , or 101,325 pascals in the metric system. A 
Celsius degree is equal to 1/100 of the difference 
between the freezing and boiling temperatures of 
water at 1 atm. 

The Celsius scale is sometimes called the 
centigrade scale, because it is divided into 100 
degrees, cent being a Latin root meaning “hun- 
dred.” By international convention, its values 
were refined in 1948, when the scale was rede- 
fined in terms of temperature change for an ideal 
gas, as well as the triple point of water. (Triple 

SCIENCE OF EVERYDAY THINGS 


point is the temperature and pressure at which a 
substance is at once a solid, liquid, and vapor.) As 
a result of these refinements, the boiling point of 
water on the Celsius scale is actually 99.975°. This 
represents a difference equal to about 1 part in 
4,000 — hardly significant in daily life, though a 
significant change from the standpoint of 
the precise measurements made in scientific 
laboratories. 

k e lv i n . In about 1787, French physicist 
and chemist J. A. C. Charles (1746-1823) made 
an interesting discovery: that at 0°C, the volume 
of gas at constant pressure drops by 1/273 for 
every Celsius degree drop in temperature. This 
seemed to suggest that the gas would simply dis- 
appear if cooled to -273°C, which, of course, 
made no sense. In any case, the gas would most 
likely become first a liquid, and then a solid, long 
before it reached that temperature. 

The man who solved the quandary raised by 
Charles’s discovery was born a year after 
Charles — who also formulated Charles’s law — 
died. He was William Thomson, Lord Kelvin 
(1824-1907), and in 1848, he put forward the 
suggestion that it was molecular translational 
energy, and not volume, that would become zero 
at -273°C. He went on to establish what came to 
be known as the Kelvin scale. 

Sometimes known as the absolute tempera- 
ture scale, the Kelvin scale is based not on the 
freezing point of water, but on absolute zero — 
the temperature at which molecular motion 
comes to a virtual stop. This is -273.15°C 
(-459.67°F), which in the Kelvin scale is designat- 
ed as OK. (Kelvin measures do not use the term or 
symbol for “degree.”) 

Though scientists normally use metric or SI 
measures, they prefer the Kelvin scale to Celsius, 
because the absolute temperature scale is directly 
related to average molecular translational energy. 
Thus, if the Kelvin temperature of an object is 
doubled, this means that its average molecular 
translational energy has doubled as well. The 
same cannot be said if the temperature were dou- 
bled from, say, 10°C to 20°C, or from 40°C to 
80°F, since neither the Celsius nor the Fahrenheit 
scale is based on absolute zero. 

conversions. The Kelvin scale is, 
however, closely related to the Celsius scale, in 
that a difference of 1 degree measures the same 
amount of temperature in both. Therefore, Cel- 
sius temperatures can be converted to Kelvins by 

SCIENCE OF EVERYDAY THINGS 


adding 273.15. There is also an absolute temper- 
ature scale that uses Fahrenheit degrees. This is 
the Rankine scale, created by Scottish engineer 
William Rankine (1820-1872), but it is seldom 
used today: scientists and others who desire 
absolute temperature measures prefer the preci- 
sion and simplicity of the Celsius-based Kelvin 
scale. 

Conversion between Celsius and Fahrenheit 
figures is a bit more challenging. To convert a 
temperature from Celsius to Fahrenheit, multiply 
by 9/5 and add 32. It is important to perform the 
steps in that order, because reversing them will 
produce a wrong answer. Thus, 100°C multiplied 
by 9/5 or 1 .8 equals 180, which, when added to 32 
equals 212°F. Obviously, this is correct, since 
100°C and 212°F each represent the boiling point 
of water. But, if one adds 32 to 100°, then multi- 
plies it by 9/5, the result is 237. 6°F — an incorrect 
answer. 

For converting Fahrenheit temperatures to 
Celsius, there are also two steps, involving multi- 
plication and subtraction, but the order is 
reversed. Here, the subtraction step is performed 
before the multiplication step: thus, 32 is sub- 
tracted from the Fahrenheit temperature, then 
the result is multiplied by 5/9. Beginning with 
212°F, if 32 is subtracted, this equals 180. Multi- 
plied by 5/9, the result is 100°C — the correct 
answer. 

One reason the conversion formulae use 
fractions instead of decimal fractions (what most 
people simply call “decimals”) is that 5/9 is a 
repeating decimal fraction (0.55555....) Further- 
more, the symmetry of 5/9 and 9/5 makes mem- 
orization easy. One way to remember the formu- 
la is that Fahrenheit is multiplied by a /faction — 
since 5/9 is a real fraction, whereas 9/5 is actually 
a whole number plus a fraction. 

Thermometers 

As discussed earlier, with regard to the early his- 
tory of the thermometer, it is important that the 
glass tube be kept sealed; otherwise, atmospheric 
pressure contributes to inaccurate readings, 
because it influences the movement of the ther- 
mometric medium. Also important is the choice 
of the thermometric medium itself. 

Water quickly proved unreliable, due to its 
unusual properties: it does not expand uniform- 
ly with a rise in temperature, or contract uni- 
formly with a lowered temperature. Rather, it 

VDLUME 2: REAL-LIFE PHYSICS 


Temperature 


24 1 


Temperature 


KEY TERMS 


absolute zero: The temperature, 

defined as OK on the Kelvin scale, at which 
the motion of molecules in a solid virtual- 
ly ceases. 

Celsius scale: A scale of tempera- 

ture, sometimes known as the centigrade 
scale, created in 1742 by Swedish 
astronomer Anders Celsius (1701-1744). 
The Celsius scale establishes the freezing 
and boiling points of water at 0° and 100°, 
respectively. To convert a temperature from 
the Celsius to the Fahrenheit scale, multi- 
ply by 9/5 and add 32. The Celsius scale is 
part of the metric system used by most 
non-English speaking countries today. 
Though the worldwide scientific commu- 
nity uses the metric or SI system for most 
measurements, scientists prefer the related 
Kelvin scale. 

Fahrenheit scale: The oldest of 

the temperature scales still used in Western 
nations today, created in 1714 by German 
physicist Daniel Fahrenheit (1686-1736). 


The Fahrenheit scale establishes the freez- 
ing and boiling points of water at 32° and 
212° respectively. To convert a temperature 
from the Fahrenheit to the Celsius scale, 
subtract 32 and multiply by 5/9. Most Eng- 
lish-speaking countries use the Fahrenheit 
scale. 

heat: Internal thermal energy that 

flows from one body of matter to another. 

kelvin scale: Established by 

William Thomson, Lord Kelvin (1824- 
1907), the Kelvin scale measures tempera- 
ture in relation to absolute zero, or OK. 
(Units in the Kelvin system, known as 
Kelvins, do not include the word or symbol 
for degree.) The Kelvin and Celsius scales 
are directly related; hence, Celsius temper- 
atures can be converted to Kelvins by 
adding 273.15. The Kelvin scale is used 
almost exclusively by scientists. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 


| 24Z 


reaches its maximum density at 39.2°F (4°C), and 
is less dense both above and below that tempera- 
ture. Therefore, alcohol, which responds in a 
much more uniform fashion to changes in tem- 
perature, took its place. 

mercury thermometers. 

Alcohol is still used in thermometers today, but 
the preferred thermometric medium is mercury. 
As noted earlier, its advantages include a much 
higher boiling point, a tendency not to stick to 
glass, and a silvery color that makes its levels easy 
to gauge visually. Like alcohol, mercury expands 
at a uniform rate with an increase in tempera- 
ture: hence, the higher the temperature, the high- 
er the mercury stands in the thermometer. 

In a typical mercury thermometer, mercury 
is placed in a long, narrow sealed tube called a 
capillary. The capillary is inscribed with figures 

volume z: real-life physics 


for a calibrated scale, usually in such a way as to 
allow easy conversions between Fahrenheit and 
Celsius. A thermometer is calibrated by measur- 
ing the difference in height between mercury at 
the freezing point of water, and mercury at the 
boiling point of water. The interval between 
these two points is then divided into equal incre- 
ments — 180, as we have seen, for the Fahrenheit 
scale, and 100 for the Celsius scale. 

electric thermometers. 

Faster temperature measures can be obtained by 
thermometers using electricity. All matter dis- 
plays a certain resistance to electrical current, a 
resistance that changes with temperature. There- 
fore, a resistance thermometer uses a fine wire 
wrapped around an insulator, and when a change 
in temperature occurs, the resistance in the wire 
changes as well. This makes possible much quick- 

SCIENCE OF EVERYDAY THINGS 



Temperature 


KEY TERMS continued 


MOLECULAR TRANSLATIONAL EN- 
ERGY: The kinetic energy in a system 

produced by the movement of molecules 
in relation to one another. 

s yste m : In physics, the term “system” 

usually refers to any set of physical interac- 
tions, or any material body, isolated from 
the rest of the universe. Anything outside 
of the system, including all factors and 
forces irrelevant to a discussion of that sys- 
tem, is known as the environment. 

temperature: A measure of the 

average kinetic energy — or molecular 
translational energy in a system. Differ- 
ences in temperature determine the direc- 
tion of internal energy flow between two 
systems when heat is being transferred. 

thermal energy: Heat energy, a 

form of kinetic energy produced by the 
movement of atomic or molecular parti- 
cles. The greater the movement of these 
particles, the greater the thermal energy. 


THERMAL EQUILIBRIUM: The State 

that exists when two systems have the same 
temperature. As a result, there is no 
exchange of heat between them. 

thermodynamics: The study of 

the relationships between heat, work, and 
energy. 

THERMDMETRIC MEDIUM: A Sub- 

stance whose properties change with tem- 
perature. A mercury or alcohol thermome- 
ter measures such changes. 

thermometer: A device that gauges 

temperature by measuring a temperature- 
dependent property, such as the expansion 
of a liquid in a sealed tube, or resistance to 
electric current. 

triple point: The temperature and 

pressure at which a substance is at once a 
solid, liquid, and vapor. 

vacuum: Space entirely devoid of 

matter, including air. 


er temperature readings than those offered by a 
thermometer containing a traditional thermo- 
metric medium. 

Resistance thermometers are highly reliable, 
but expensive, and are used primarily for very 
precise measurements. More practical for every- 
day use is a thermistor, which also uses the prin- 
ciple of electric resistance, but is much simpler 
and less expensive. Thermistors are used for pro- 
viding measurements of the internal temperature 
of food, for instance, and for measuring human 
body temperature. 

Another electric temperature-measurement 
device is a thermocouple. When wires of two dif- 
ferent materials are connected, this creates a 
small level of voltage that varies as a function of 
temperature. A typical thermocouple uses two 
junctions: a reference junction, kept at some con- 

SCIENCE DF EVERYDAY THINGS 


stant temperature, and a measurement junction. 
The measurement junction is applied to the item 
whose temperature is to be measured, and any 
temperature difference between it and the refer- 
ence junction registers as a voltage change, which 
is measured with a meter connected to the sys- 
tem. 

OTHER TYPES OF THERMOME- 
TER. A pyrometer also uses electromagnetic 
properties, but of a very different kind. Rather 
than responding to changes in current or voltage, 
the pyrometer is a gauge that responds to visible 
and infrared radiation. Temperature and color 
are closely related: thus, it is no accident that 
greens, blues, and purples, at one end of the visi- 
ble light spectrum, are associated with coolness, 
while reds, oranges, and yellows at the other end 
are associated with heat. As with the thermocou- 

VDLUME 2: REAL-LIFE PHYSICS 


243 



Temperature 


pie, a pyrometer has both a reference element 
and a measurement element, which compares 
light readings between the reference filament and 
the object whose temperature is being measured. 

Still other thermometers, such as those in an 
oven that tell the user its internal temperature, 
are based on the expansion of metals with heat. 
In fact, there are a wide variety of thermometers, 
each suited to a specific purpose. A pyrometer, 
for instance, is good for measuring the tempera- 
ture of an object that the thermometer itself does 
not touch. 

WHERE TO LEARN MORE 

About Temperature (Web site). 

<http://www.unidata.ucar.edu/staff/blynds/tmp. 
html> (April 18, 2001). 

About Temperature Sensors (Web site), <http://www.tem- 
peratures.com> (April 18, 2001). 


Gardner, Robert. Science Projects About Methods of Mea- 
suring. Berkeley Heights, N.J.: Enslow Publishers, 
2000. 

Maestro, Betsy and Giulio Maestro. Temperature and You. 
New York: Macmillan/McGraw-Hill School Publish- 
ing, 1990. 

Megaconverter (Web site). 

<http://www.megaconverter.com> (April 18,2001). 

NPL: National Physics Laboratory: Thermal Stuff: Begin- 
ners’ Guides (Web site). 

<http://www.npl.co.uk/npl/cbtm/thermal/stuff/ 
guides.html> (April 18, 2001). 

Royston, Angela. Hot and Cold. Chicago: Heinemann 
Library, 2001. 

Santrey, Laurence. Heat. Illustrated by Lloyd Birming- 
ham. Mahwah, N.J.: Troll Associates, 1985. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

Walpole, Brenda. Temperature. Illustrated by Chris Fair- 
clough and Dennis Tinkler. Milwaukee, WI: Gareth 
Stevens Publishing, 1995. 


| 244 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


THERMAL EXPANSION 


C □ N C E PT 

Most materials are subject to thermal expansion: 
a tendency to expand when heated, and to con- 
tract when cooled. For this reason, bridges are 
built with metal expansion joints, so that they 
can expand and contract without causing faults 
in the overall structure of the bridge. Other 
machines and structures likewise have built-in 
protection against the hazards of thermal expan- 
sion. But thermal expansion can also be advanta- 
geous, making possible the workings of ther- 
mometers and thermostats. 

H □ W IT WORKS 

Molecular Translational 
Energy 

In scientific terms, heat is internal energy that 
flows from a system of relatively high tempera- 
ture to one at a relatively low temperature. The 
internal energy itself, identified as thermal ener- 
gy, is what people commonly mean when they 
say “heat.” A form of kinetic energy due to the 
movement of molecules, thermal energy is some- 
times called molecular translational energy. 

Temperature is defined as a measure of the 
average molecular translational energy in a sys- 
tem, and the greater the temperature change for 
most materials, as we shall see, the greater the 
amount of thermal expansion. Thus, all these 
aspects of “heat” — heat itself (in the scientific 
sense), as well as thermal energy, temperature, 
and thermal expansion — are ultimately affected 
by the motion of molecules in relation to one 
another. 

SCIENCE □ E EVERYDAY THINGS 


MOLECULAR MOTION AND 

Newtonian physics. In general, the 
kinetic energy created by molecular motion can 
be understood within the framework of classical 
physics — that is, the paradigm associated with 
Sir Isaac Newton (1642-1727) and his laws of 
motion. Newton was the first to understand the 
physical force known as gravity, and he explained 
the behavior of objects within the context of 
gravitational force. Among the concepts essential 
to an understanding of Newtonian physics are 
the mass of an object, its rate of motion (whether 
in terms of velocity or acceleration), and the dis- 
tance between objects. These, in turn, are all 
components central to an understanding of how 
molecules in relative motion generate thermal 
energy. 

The greater the momentum of an object — 
that is, the product of its mass multiplied by its 
rate of velocity — the greater the impact it has on 
another object with which it collides. The 
greater, also, is its kinetic energy, which is equal 
to one-half its mass multiplied by the square of 
its velocity. The mass of a molecule, of course, is 
very small, yet if all the molecules within an 
object are in relative motion — many of them col- 
liding and, thus, transferring kinetic energy — 
this is bound to lead to a relatively large amount 
of thermal energy on the part of the larger object. 

MDLECULAR ATTRACTION AND 

phases df matter. Yet, precisely 
because molecular mass is so small, gravitational 
force alone cannot explain the attraction 
between molecules. That attraction instead must 
be understood in terms of a second type of 
force — electromagnetism — discovered by Scot- 
tish physicist James Clerk Maxwell (1831-1879). 
The details of electromagnetic force are not 

VDLUME Z: REAL-LIFE PHYSICS 




| 246 


Because steel has a relatively high coefficient of thermal expansion, standard railroad tracks are 

CONSTRUCTED SO THAT THEY CAN SAFELY EXPAND ON A HOT DAY WITHOUT DERAILING THE TRAINS TRAVELING OVER 

them. (Milepost 92 1/2/Corbis. Reproduced by permission.) 


important here; it is necessary only to know that 
all molecules possess some component of electri- 
cal charge. Since like charges repel and opposite 
charges attract, there is constant electromagnetic 
interaction between molecules, and this pro- 
duces differing degrees of attraction. 

The greater the relative motion between 
molecules, generally speaking, the less their 
attraction toward one another. Indeed, these two 
aspects of a material — relative attraction and 
motion at the molecular level — determine 
whether that material can be classified as a solid, 
liquid, or gas. When molecules move slowly in 
relation to one another, they exert a strong 
attraction, and the material of which they are a 

VDLUME 2: REAL-LIFE PHYSICS 


part is usually classified as a solid. Molecules of 
liquid, on the other hand, move at moderate 
speeds, and therefore exert a moderate attrac- 
tion. When molecules move at high speeds, they 
exert little or no attraction, and the material is 
known as a gas. 

Predicting Thermal 
Expansion 

COEFFICIENT OF LINEAR EX- 
PANSION. A coefficient is a number that 
serves as a measure for some characteristic or 
property. It may also be a factor against which 
other values are multiplied to provide a desired 
result. For any type of material, it is possible to 

SCIENCE OF EVERYDAY THINGS 





A MAN ICE FISHING IN MONTANA. BECAUSE OF THE UNIQUE THERMAL EXPANSION PROPERTIES OF WATER, ICE FORMS 
AT THE TOP OF A LAKE RATHER THAN THE BOTTOM, THUS ALLOWING MARINE LIFE TO CONTINUE LIVING BELOW ITS 

surface during the winter. (Corbis. Reproduced by permission.) 


calculate the degree to which that material will 
expand or contract when exposed to changes in 
temperature. This is known, in general terms, as 
its coefficient of expansion, though, in fact, there 
are two varieties of expansion coefficient. 

The coefficient of linear expansion is a con- 
stant that governs the degree to which the length 
of a solid will change as a result of an alteration 
in temperature For any given substance, the coef- 
ficient of linear expansion is typically a number 
expressed in terms of 10- 5 /°C. In other words, the 
value of a particular solid’s linear expansion 
coefficient is multiplied by 0.00001 per °C. (The 
°C in the denominator, shown in the equation 
below, simply “drops out” when the coefficient of 

SCIENCE OF EVERYDAY THINGS 


linear expansion is multiplied by the change in 
temperature.) 

For quartz, the coefficient of linear expan- 
sion is 0.05. By contrast, iron, with a coefficient 
of 1.2, is 24 times more likely to expand or con- 
tract as a result of changes in temperature. (Steel 
has the same value as iron.) The coefficient for 
aluminum is 2.4, twice that of iron or steel. This 
means that an equal temperature change will 
produce twice as much change in the length of a 
bar of aluminum as for a bar of iron. Lead is 
among the most expansive solid materials, with a 
coefficient equal to 3.0. 

CALCULATING LINEAR EX- 
PANSION. The linear expansion of a given 

VDLUME 2: REAL-LIFE PHYSICS 


24V 


Thermal 

Expansion 


| 243 


solid can be calculated according to the formula 
8 L = clLqAT. The Greek letter delta (d) means “a 
change in”; hence, the first figure represents 
change in length, while the last figure in the 
equation stands for change in temperature. The 
letter a is the coefficient of linear expansion, and 
L 0 is the original length. 

Suppose a bar of lead 5 meters long experi- 
ences a temperature change of 10°C; what will its 
change in length be? To answer this, a (3.0 • 
10’ 5 /°C) must be multiplied by L 0 (5 m) and 8 T 
(10°C). The answer should be 150 & 10- 5 m, or 
1.5 mm. Note that this is simply a change in 
length related to a change in temperature: if the 
temperature is raised, the length will increase, 
and if the temperature is lowered by 10°C, the 
length will decrease by 1.5 mm. 

volume expansion. Obviously, 
linear equations can only be applied to solids. 
Liquids and gases, classified together as fluids, 
conform to the shape of their container; hence, 
the “length” of any given fluid sample is the same 
as that of the solid that contains it. Fluids are, 
however, subject to volume expansion — that is, a 
change in volume as a result of a change in tem- 
perature. 

To calculate change in volume, the formula 
is very much the same as for change in length; 
only a few particulars are different. In the formu- 
la SV = bV 0 8T, the last term, again, means 
change in temperature, while $V means change 
in volume and V Q is the original volume. The let- 
ter b refers to the coefficient of volume expan- 
sion. The latter is expressed in terms of 1CH/ 0 C, 
or 0.0001 per °C. 

Glass has a very low coefficient of volume 
expansion, 0.2, and that of Pyrex glass is 
extremely low — only 0.09. For this reason, items 
made of Pyrex are ideally suited for cooking. Sig- 
nificantly higher is the coefficient of volume 
expansion for glycerin, an oily substance associ- 
ated with soap, which expands proportionally to 
a factor of 5. 1 . Even higher is ethyl alcohol, with 
a volume expansion coefficient of 7.5. 

REAL-LIFE 
A P P L I C AT I □ N S 

Liquids 

Most liquids follow a fairly predictable pattern of 
gradual volume increase, as a response to an 

VDLUME 2: REAL-LIFE PHYSICS 


increase in temperature, and volume decrease, in 
response to a decrease in temperature. Indeed, 
the coefficient of volume expansion for a liquid 
generally tends to be higher than for a solid, 
and — with one notable exception discussed 
below — a liquid will contract when frozen. 

The behavior of gasoline pumped on a hot 
day provides an example of liquid thermal 
expansion in response to an increase in tempera- 
ture. When it comes from its underground tank 
at the gas station, the gasoline is relatively cool, 
but it will warm when sitting in the tank of an 
already warm car. If the car’s tank is filled and the 
vehicle left to sit in the sun — in other words, if 
the car is not driven after the tank is filled — the 
gasoline might very well expand in volume fas- 
ter than the fuel tank, overflowing onto the 
pavement. 

engine cdglant. Another exam- 
ple of thermal expansion on the part of a liquid 
can be found inside the car’s radiator. If the radi- 
ator is “topped off” with coolant on a cold day, an 
increase in temperature could very well cause the 
coolant to expand until it overflows. In the past, 
this produced a problem for car owners, because 
car engines released the excess volume of coolant 
onto the ground, requiring periodic replacement 
of the fluid. 

Later-model cars, however, have an overflow 
container to collect fluid released as a result of 
volume expansion. As the engine cools down 
again, the container returns the excess fluid to the 
radiator, thus, “recycling” it. This means that 
newer cars are much less prone to overheating as 
older cars. Combined with improvements in 
radiator fluid mixtures, which act as antifreeze in 
cold weather and coolant in hot, the “recycling” 
process has led to a significant decrease in break- 
downs related to thermal expansion. 

water. One good reason not to use pure 
water in one’s radiator is that water has a far 
higher coefficient of volume expansion than a 
typical engine coolant. This can be particularly 
hazardous in cold weather, because frozen water 
in a radiator could expand enough to crack the 
engine block. 

In general, water — whose volume expansion 
coefficient in the liquid state is 2.1, and 0.5 in the 
solid state — exhibits a number of interesting 
characteristics where thermal expansion is con- 
cerned. If water is reduced from its boiling 
point— 21 2°F (100°C) to 39.2°F (4°C) it will 

SCIENCE OF EVERYDAY THINGS 


steadily contract, like any other substance 
responding to a drop in temperature. Normally, 
however, a substance continues to become denser 
as it turns from liquid to solid; but this does not 
occur with water. 

At 32.9°F, water reaches it maximum densi- 
ty, meaning that its volume, for a given unit of 
mass, is at a minimum. Below that temperature, 
it “should” (if it were like most types of matter) 
continue to decrease in volume per unit of mass, 
but, in fact, it steadily begins to expand. Thus, it 
is less dense, with a greater volume per unit of 
mass, when it reaches the freezing point. It is for 
this reason that when pipes freeze in winter, they 
often burst — explaining why a radiator filled 
with water could be a serious problem in very 
cold weather. 

In addition, this unusual behavior with 
regard to thermal expansion and contraction 
explains why ice floats: solid water is less dense 
than the liquid water below it. As a result, frozen 
water stays at the top of a lake in winter; since ice 
is a poor conductor of heat, energy cannot escape 
from the water below it in sufficient amounts to 
freeze the rest of the lake water. Thus, the water 
below the ice stays liquid, preserving plant and 
animal life. 

Gases 

the bas laws. As discussed, liq- 
uids expand by larger factors than solids do. 
Given the increasing amount of molecular kinet- 
ic energy for a liquid as compared to a solid, and 
for a gas as compared to a liquid, it should not be 
surprising, then, to learn that gases respond to 
changes in temperature with a volume change 
even greater than that of liquids. Of course, 
where a gas is concerned, “volume” is more diffi- 
cult to measure, because a gas simply expands to 
fill its container. In order for the term to have any 
meaning, pressure and temperature must be 
specified as well. 

A number of the gas laws describe the three 
parameters for gases: volume, temperature, and 
pressure. Boyle’s law, for example, holds that in 
conditions of constant temperature, an inverse 
relationship exists between the volume and pres- 
sure of a gas: the greater the pressure, the less the 
volume, and vice versa. Even more relevant to the 
subject of thermal expansion is Charles’s law. 

Charles’s law states that when pressure is 
kept constant, there is a direct relationship 

SCIENCE BF EVERYDAY THINGS 


between volume and temperature. As a gas heats 
up, its volume increases, and when it cools down, 
its volume reduces accordingly. Thus, if an air 
mattress is filled in an air-conditioned room, and 
the mattress is then taken to the beach on a hot 
day, the air inside will expand. Depending on 
how much its volume increases, the expansion of 
the hot air could cause the mattress to “pop.” 

VBLUME BAS THERMOME- 
TERS. Whereas liquids and solids vary signif- 
icantly with regard to their expansion coeffi- 
cients, most gases follow more or less the same 
pattern of expansion in response to increases in 
temperature. The predictable behavior of gases in 
these situations led to the development of the 
constant gas thermometer, a highly reliable 
instrument against which other thermometers — 
including those containing mercury (see 
below) — are often gauged. 

In a volume gas thermometer, an empty 
container is attached to a glass tube containing 
mercury. As gas is released into the empty con- 
tainer, this causes the column of mercury to 
move upward. The difference between the former 
position of the mercury and its position after the 
introduction of the gas shows the difference 
between normal atmospheric pressure and the 
pressure of the gas in the container. It is, then, 
possible to use the changes in volume on the part 
of the gas as a measure of temperature. The 
response of most gases, under conditions of low 
pressure, to changes in temperature is so uniform 
that volume gas thermometers are often used to 
calibrate other types of thermometers. 

S OLI DS 

Many solids are made up of crystals, regular 
shapes composed of molecules joined to one 
another as though on springs. A spring that is 
pulled back, just before it is released, is an exam- 
ple of potential energy, or the energy that an 
object possesses by virtue of its position. For a 
crystalline solid at room temperature, potential 
energy and spacing between molecules are rela- 
tively low. But as temperature increases and the 
solid expands, the space between molecules 
increases — as does the potential energy in the 
solid. 

In fact, the responses of solids to changes in 
temperature tend to be more dramatic, at least 
when they are seen in daily life, than are the 
behaviors of liquids or gases under conditions of 

VDLUME 2: REAL-LIFE PHYSICS 


Thermal 

Expansion 


249 


Thermal 

Expansion 


| Z5D 


thermal expansion. Of course, solids actually 
respond less to changes in temperature than flu- 
ids do; but since they are solids, people expect 
their contours to be immovable. Thus, when the 
volume of a solid changes as a result of an 
increase in thermal energy, the outcome is more 
noteworthy. 

JAR LIDS AND PDWER LINES. 

An everyday example of thermal expansion can 
be seen in the kitchen. Almost everyone has had 
the experience of trying unsuccessfully to budge 
a tight metal lid on a glass container, and after 
running hot water over the lid, finding that it 
gives way and opens at last. The reason for this is 
that the high-temperature water causes the metal 
lid to expand. On the other hand, glass — as noted 
earlier — has a low coefficient of expansion. Oth- 
erwise, it would expand with the lid, which 
would defeat the purpose of running hot water 
over it. If glass jars had a high coefficient of 
expansion, they would deform when exposed to 
relatively low levels of heat. 

Another example of thermal expansion in a 
solid is the sagging of electrical power lines on a 
hot day. This happens because heat causes them 
to expand, and, thus, there is a greater length of 
power line extending from pole to pole than 
under lower temperature conditions. It is highly 
unlikely, of course, that the heat of summer 
could be so great as to pose a danger of power 
lines breaking; on the other hand, heat can create 
a serious threat with regard to larger structures. 

expansion joints. Most large 
bridges include expansion joints, which look 
rather like two metal combs facing one another, 
their teeth interlocking. When heat causes the 
bridge to expand during the sunlight hours of a 
hot day, the two sides of the expansion joint 
move toward one another; then, as the bridge 
cools down after dark, they begin gradually to 
retract. Thus the bridge has a built-in safety zone; 
otherwise, it would have no room for expansion 
or contraction in response to temperature 
changes. As for the use of the comb shape, this 
staggers the gap between the two sides of the 
expansion joint, thus minimizing the bump 
motorists experience as they drive over it. 

Expansion joints of a different design can 
also be found in highways, and on “highways” of 
rail. Thermal expansion is a particularly serious 
problem where railroad tracks are concerned, 
since the tracks on which the trains run are made 

VDLUME 2: REAL-LIFE PHYSICS 


of steel. Steel, as noted earlier, expands by a fac- 
tor of 12 parts in 1 million for every Celsius 
degree change in temperature, and while this 
may not seem like much, it can create a serious 
problem under conditions of high temperature. 

Most tracks are built from pieces of steel 
supported by wooden ties, and laid with a gap 
between the ends. This gap provides a buffer for 
thermal expansion, but there is another matter to 
consider: the tracks are bolted to the wooden ties, 
and if the steel expands too much, it could pull 
out these bolts. Hence, instead of being placed in 
a hole the same size as the bolt, the bolts are fit- 
ted in slots, so that there is room for the track to 
slide in place slowly when the temperature rises. 

Such an arrangement works agreeably for 
trains that run at ordinary speeds: their wheels 
merely make a noise as they pass over the gaps, 
which are rarely wider than 0.5 in (0.013 m). A 
high-speed train, however, cannot travel over 
irregular track; therefore, tracks for high-speed 
trains are laid under conditions of relatively high 
tension. Hydraulic equipment is used to pull sec- 
tions of the track taut; then, once the track is 
secured in place along the cross ties, the tension 
is distributed down the length of the track. 

Thermometers and 
Thermostats 

MERCURY IN THERMOMETERS. 

A thermometer gauges temperature by measur- 
ing a temperature-dependent property. A ther- 
mostat, by contrast, is a device for adjusting the 
temperature of a heating or cooling system. Both 
use the principle of thermal expansion in their 
operation. As noted in the example of the metal 
lid and glass jar above, glass expands little with 
changes in temperature; therefore, it makes an 
ideal container for the mercury in a thermome- 
ter. As for mercury, it is an ideal thermometric 
medium — that is, a material used to gauge tem- 
perature — for several reasons. Among these is a 
high boiling point, and a highly predictable, uni- 
form response to changes in temperature. 

In a typical mercury thermometer, mercury 
is placed in a long, narrow sealed tube called a 
capillary. Because it expands at a much faster rate 
than the glass capillary, mercury rises and falls 
with the temperature. A thermometer is calibrat- 
ed by measuring the difference in height between 
mercury at the freezing point of water, and mer- 
cury at the boiling point of water. The interval 

SCIENCE DF EVERYDAY THINGS 


Thermal 

Expansion 


KEY TERMS 


coefficient: A number that serves 

as a measure for some characteristic or 
property. A coefficient may also be a factor 
against which other values are multiplied 
to provide a desired result. 

COEFFICIENT OF LINEAR EXPAN- 
SION: A figure, constant for any partic- 

ular type of solid, used in calculating the 
amount by which the length of that solid 
will change as a result of temperature 
change. For any given substance, the coeffi- 
cient of linear expansion is typically a 
number expressed in terms of 10- 5 /°C. 

COEFFICIENT OF VOLUME EXPAN- 
SION: A figure, constant for any partic- 

ular type of material, used in calculating 
the amount by which the volume of that 
material will change as a result of tempera- 
ture change. For any given substance, the 
coefficient of volume expansion is typical- 
ly a number expressed in terms of 10- 4 / o C. 

heat: Internal thermal energy that 

flows from one body of matter to another. 

kinetic energy: The energy that 

an object possesses by virtue of its motion. 

MOLECULAR TRANSLATIONAL EN- 
ERGY: The kinetic energy in a system 


produced by the movement of molecules 
in relation to one another. 

potential energy: The energy 

that an object possesses by virtue of its 
position. 

system: In physics, the term “system” 

usually refers to any set of physical interac- 
tions, or any material body, isolated from 
the rest of the universe. Anything outside 
of the system, including all factors and 
forces irrelevant to a discussion of that sys- 
tem, is known as the environment. 

temperature: A measure of the 

average kinetic energy — or molecular 
translational energy in a system. Differ- 
ences in temperature determine the direc- 
tion of internal energy flow between two 
systems when heat is being transferred. 

thermal energy: Heat energy, a 

form of kinetic energy produced by the 
movement of atomic or molecular parti- 
cles. The greater the movement of these 
particles, the greater the thermal energy. 

thermal expansidn: A property 

in all types of matter that display a tenden- 
cy to expand when heated, and to contract 
when cooled. 


between these two points is then divided into 
equal increments in accordance with one of the 
well-known temperature scales. 

the bimetallic strip in 
thermos tat s . In a thermostat, the cen- 
tral component is a bimetallic strip, consisting of 
thin strips of two different metals placed back to 
back. One of these metals is of a kind that pos- 
sesses a high coefficient of linear expansion, 
while the other metal has a low coefficient. A 
temperature increase will cause the side with a 
higher coefficient to expand more than the side 

SCIENCE GF EVERYDAY THINGS 


that is less responsive to temperature changes. As 
a result, the bimetallic strip will bend to one side. 

When the strip bends far enough, it will 
close an electrical circuit, and, thus, direct the air 
conditioner to go into action. By adjusting the 
thermostat, one varies the distance that the 
bimetallic strip must be bent in order to close the 
circuit. Once the air in the room reaches the 
desired temperature, the high- coefficient metal 
will begin to contract, and the bimetallic strip 
will straighten. This will cause an opening of the 
electrical circuit, disengaging the air conditioner. 

VOLUME 2: REAL-LIFE PHYSICS 


25 1 



Thermal 

Expansion 


In cold weather, when the temperature-con- 
trol system is geared toward heating rather than 
cooling, the bimetallic strip acts in much the 
same way — only this time, the high-coefficient 
metal contracts with cold, engaging the heater. 
Another type of thermostat uses the expansion of 
a vapor rather than a solid. In this case, heating of 
the vapor causes it to expand, pushing on a set of 
brass bellows and closing the circuit, thus, engag- 
ing the air conditioner. 

WHERE TO LEARN MORE 

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison- 
Wesley, 1991. 

“Comparison of Materials: Coefficient of Thermal Expan- 
sion” (Web site). <http://www.handyharmancanada. 
com/TheBrazingBook/comparis.html> (April 21, 
2001 ). 

Encyclopedia of Thermodynamics (Web site). <http://the- 
rion.minpet.unibas.ch/minpet/groups/thermodict/> 
(April 12,2001). 


Fleisher, Paul. Matter and Energy: Principles of Matter 
and Thermodynamics. Minneapolis, MN: Lerner Pub- 
lications, 2002. 

NPL: National Physics Laboratory: Thermal Stuff: Begin- 
ners’ Guides (Web site), <http://www.npl.co.uk/ 
npl/cbtm/thermal/stuff/guides.html> (April 18, 
2001). 

Royston, Angela. Hot and Cold. Chicago: Heinemann 
Library, 2001. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

“Thermal Expansion Measurement” (Web site). 

<http://www.measurementsgroup.com/guide/tn/ 
tn513/513intro.html> (April 21, 2001). 

“Thermal Expansion of Solids and Liquids” (Web site). 
<http://www.physics.mun.ca/~gquirion/P2053/ 
htmll9b/> (April 21, 2001). 

Walpole, Brenda. Temperature. Illustrated by Chris Fair- 
clough and Dennis Tinkler. Milwaukee, WI: Gareth 
Stevens Publishing, 1995. 


25Z 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 


SCIENCE DF EVERYDAY THINGS 

REAL-LIFE PHYSICS 


WAVE MOTION 
AND OSCILL AT [ O N 


WAVE MOTION 


O S C I L L AT I O N 


FREQUENCY 


RESONANCE 


NTERFERENCE 


DIFFRACTION 


DOPPLER EFFECT 


Z53 




WAV E 


M □ T I □ N 


C □ N C E PT 

Wave motion is activity that carries energy from 
one place to another without actually moving 
any matter. Studies of wave motion are most 
commonly associated with sound or radio trans- 
missions, and, indeed, these are among the most 
common forms of wave activity experienced in 
daily life. Then, of course, there are waves on the 
ocean or the waves produced by an object falling 
into a pool of still water — two very visual exam- 
ples of a phenomenon that takes place every- 
where in the world around us. 

H □ W IT WDRKS 

Related Fdrms of Mqtiein 

In wave motion, energy — the ability to perform 
work, or to exert force over distance — is trans- 
mitted from one place to another without actual- 
ly moving any matter along the wave. In some 
types of waves, such as those on the ocean, it 
might seem as though matter itself has been dis- 
placed; that is, it appears that the water has actu- 
ally moved from its original position. In fact, this 
is not the case: molecules of water in an ocean 
wave move up and down, but they do not actual- 
ly travel with the wave itself. Only the energy is 
moved. 

A wave is an example of a larger class of reg- 
ular, repeated, and/or back-and- forth types of 
motion. As with wave motion, these varieties of 
movement may or may not involve matter, but, 
in any case, the key component is not matter, but 
energy. Broadest among these is periodic motion, 
or motion that is repeated at regular intervals 
called periods. A period might be the amount of 

SCIENCE □ F EVERYDAY THINGS 


time that it takes an object orbiting another (as, 
for instance, a satellite going around Earth) to 
complete one cycle of orbit. With wave motion, a 
period is the amount of time required to com- 
plete one full cycle of the wave, from trough to 
crest and back to trough. 

harmdnic motion. Harmonic 
motion is the repeated movement of a particle 
about a position of equilibrium, or balance. In 
harmonic motion — or, more specifically, simple 
harmonic motion — the object moves back and 
forth under the influence of a force directed 
toward the position of equilibrium, or the place 
where the object stops if it ceases to be in motion. 
A familiar example of harmonic motion, to any- 
one who has seen an old movie with a cliched 
depiction of a hypnotist, is the back-and-forth 
movement of the hypnotist’s watch, as he tries to 
control the mind of his patient. 

One variety of harmonic motion is vibra- 
tion, which wave motion resembles in some 
respects. Both wave motion and vibration are 
periodic, involving the regular repetition of a cer- 
tain form of movement. In both, there is a con- 
tinual conversion and reconversion between 
potential energy (the energy of an object due to 
its position, as for instance with a sled at the top 
of a hill) and kinetic energy (the energy of an 
object due to its motion, as with the sled when 
sliding down the hill.) The principal difference 
between vibration and wave motion is that, in 
the first instance, the energy remains in place, 
whereas waves actually transport energy from 
one place to another. 

□ s c i l l at ion. Oscillation is a type of 
harmonic motion, typically periodic, in one or 
more dimensions. Suppose a spring is fixed in 

VDLUME Z: REAL-LIFE PHYSICS 


2 5 5 



Wave Motion 


| 256 



Heinrich He rtz . (Hulton-Deutsch Collection/Corbis. Reproduced 
by permission.) 

place to a ceiling, such that it hangs downward. 
At this point, the spring is in a position of equi- 
librium. Now, consider what happens if the 
spring is grasped at a certain point and lifted, 
then let go. It will, of course, fall downward with 
the force of gravity until it comes to a stop — but 
it will not stop at the earlier position of equilib- 
rium. Instead, it will continue downward to a 
point of maximum tension, where it possesses 
maximum potential energy as well. Then, it will 
spring upward again, and as it moves, its kinetic 
energy increases, while potential energy decreas- 
es. At the high point of this period of oscillation, 
the spring will not be as high as it was before it 
was originally released, but it will be higher than 
the position of equilibrium. 

Once it falls, the spring will again go lower 
than the position of equilibrium, but not as low 
as before — and so on. This is an example of oscil- 
lation. Now, imagine what happens if another 
spring is placed beside the first one, and they are 
connected by a rubber band. If just the first 
spring is disturbed, as before, the second spring 
will still move, because the energy created by the 
movement of the first spring will be transmitted 
to the second one via the rubber band. The same 
will happen if a row of springs, all side-by-side, 
are attached by multiple rubber bands, and the 

VDLUME 2: REAL-LIFE PHYSICS 


first spring is once again disturbed: the energy 
will pass through the rubber bands, from spring 
to spring, causing the entire row to oscillate. This 
is similar to what happens in the motion of a 
wave. 

Types and Properties of 
Waves 

There are some types of waves that do not follow 
regular, repeated patterns; these are discussed 
below, in the illustration concerning a string, in 
which a pulse is created and reflected. Of princi- 
pal concern here, however, is the periodic wave, a 
series of wave motions, following one after the 
other in regular succession. Examples of period- 
ic waves include waves on the ocean, sound 
waves, and electromagnetic waves. The last of 
these include visible light and radio, among 
others. 

Electromagnetic waves involve only energy; 
on the other hand, a mechanical wave involves 
matter as well. Ocean waves are mechanical 
waves; so, too, are sound waves, as well as the 
waves produced by pulling a string. It is impor- 
tant to note, again, that the matter itself is not 
moved from place to place, though it may move 
in place without leaving its position. For exam- 
ple, water molecules in the crest of an ocean wave 
rotate in the same direction as the wave, while 
those in the trough of the wave rotate in a direc- 
tion opposite to that of the wave, yet there is no 
net motion of the water: only energy is transmit- 
ted along the wave. 

FIVE PROPERTIES OF WAVES. 

There are three notable interrelated characteris- 
tics of periodic waves. One of these is wave speed, 
symbolized by v and typically calculated in 
meters per second. Another is wavelength, repre- 
sented as X (the Greek letter lambda), which is 
the distance between a crest and the adjacent 
crest, or a trough and the adjacent trough. The 
third is frequency, abbreviated as /, which is the 
number of waves passing through a given point 
during the interval of 1 second. 

Frequency is measured in terms of cycles per 
second, or Hertz (Hz), named in honor of nine- 
teenth-century German physicist Heinrich 
Rudolf Hertz (1857-1894). If a wave has a fre- 
quency of 100 Hz, this means that 100 waves are 
passing through a given point during the interval 
of 1 second. Higher frequencies are expressed in 
terms of kilohertz (kHz; 10 3 or 1,000 cycles per 

SCIENCE OF EVERYDAY THINGS 


Wave Mdti on 



Transverse waves produced by a water droplet penetrating the surface of a body of liquid. (Photograph 
by Martin Dohrn/Science Photo Library, National Audubon Society Collection/Photo Researchers, Inc. Reproduced with permission.) 


second) or megahertz (MHz; 10 6 or 1 million 
cycles per second.) 

Frequency is clearly related to wave speed, 
and there is also a relationship — though it is not 
so immediately grasped — between wavelength 
and speed. Over the interval of 1 second, a given 
number of waves pass a certain point (frequen- 
cy), and each wave occupies a certain distance 
(wavelength). Multiplied by one another, these 
two properties equal the speed of the wave. This 
can be stated as a formula: v — fk. 

Earlier, the term “period” was defined in 
terms of wave motion as the amount of time 
required to complete one full cycle of the wave. 
Period, symbolized by T, can be expressed in 
terms of frequency, and, thus, can also be related 
to the other two properties identified above. It is 
the inverse of frequency, meaning that T = 1 If. 
Furthermore, period is equal to the ratio of 
wavelength to wave speed; in other words, 
T = X/v. 

A fifth property of waves — one not mathe- 
matically related to wavelength, wave speed, fre- 
quency, or period, is amplitude. Amplitude can 
be defined as the maximum displacement of 
oscillating particles from their normal position. 
For an ocean wave, amplitude is the distance 

SCIENCE □ E EVERYDAY THINGS 


from either the crest or the trough to the level 
that the ocean would maintain if it were per- 
fectly still. 

wave shapes. When most people 
think of waves, naturally, one of the first images 
that comes to mind is that of waves on the ocean. 
These are an example of a transverse wave, or one 
in which the vibration or motion is perpendicu- 
lar to the direction the wave is moving. (Actually, 
ocean waves are simply perceived as transverse 
waves; in fact, as discussed below, their behavior 
is rather more complicated.) In a longitudinal 
wave, on the other hand, the movement of vibra- 
tion is in the same direction as the wave itself. 

Transverse waves are easier to visualize, par- 
ticularly with regard to the aspects of wave 
motion — for example, frequency and ampli- 
tude — discussed above. Yet, longitudinal waves 
can be understood in terms of a common exam- 
ple. Sound waves, for instance, are longitudinal: 
thus, when a stereo is turned up to a high vol- 
ume, the speakers vibrate in the same direction as 
the sound itself. 

A longitudinal wave may be understood as a 
series of fluctuations in density. If one were to 
take a coiled spring (such as the toy known as the 
“Slinky”) and release one end while holding the 

VDLUME 2: REAL-LIFE PHYSICS 


25V 



Wave Motion 


other, the motion of the springs would produce 
longitudinal waves. As these waves pass through 
the spring, they cause some portions of it to be 
compressed and others extended. The distance 
between each point of compression is the wave- 
length. 

Now, to return to the qualified statement 
made above: that ocean waves are an example of 
transverse waves. We perceive them as transverse 
waves, but, in fact, they are also longitudinal. In 
fact, all types of waves on the surface of a liquid 
are a combination of longitudinal and transverse, 
and are known as surface waves. Thus, if one 
drops a stone into a body of still water, waves 
radiate outward (longitudinal), but these waves 
also have a component that is perpendicular to 
the surface of the water, meaning that they are 
also transverse. 


REAL-LIFE 
A P P L I C AT I □ N S 

Pulses on a String 

There is another variety of wave, though it is 
defined in terms of behavior rather than the 
direction of disturbance. (In terms of direction, 
it is simply a variety of transverse wave.) This is a 
standing wave, produced by causing vibrations 
on a string or other piece of material whose ends 
are fixed in place. Standing waves are really a 
series of pulses that travel down the string and 
are reflected back to the point of the original dis- 
turbance. 

Suppose you hold a string in one hand, with 
the other end attached to a wall. If you give the 
string a shake, this causes a pulse — an isolated, 
non-periodic disturbance — to move down it. A 
pulse is a single wave, and the behavior of this 
lone wave helps us to understand what happens 
within the larger framework of wave motion. As 
with wave motion in general, the movement of 
the pulse involves both kinetic and potential 
energy. The tension of the string itself creates 
potential energy; then, as the movement of the 
pulse causes the string to oscillate upward and 
downward, this generates a certain amount of 
kinetic energy. 

TENSION AND REFLECTION. 

The speed of the pulse is a function of the string 
and its properties, not of the way that the pulse 


was originally delivered. The tighter the string, 
and the less its mass per unit of length, the faster 
the pulse travels down it. The greater the mass 
per unit of length, however, the greater the iner- 
tia resisting the movement of the pulse. Further- 
more, the more loosely you hold the string, the 
less it will respond to the movement of the pulse. 

In accordance with the third law of motion, 
there should be an equal and opposite reaction 
once the pulse comes into contact with the wall. 
Assuming that you are holding the string tightly, 
this reaction will be manifested in the form of an 
inverted wave, or one that is upside-down in rela- 
tion to the original pulse. In this case, the tension 
on the end attached to the support is equal and 
opposite to the tension exerted by your hand. As 
a result, the pulse comes back in the same shape 
as before, but inverted. 

If, on the other hand, you hold the other end 
of the string loosely; instead, once it reaches the 
wall, its kinetic energy will be converted into 
potential energy, which will cause the end of the 
string closest to the wall to move downward. This 
will result in sending back a pulse that is reversed 
in horizontal direction, but the same in vertical 
direction. 

In both cases, the energy in the string is 
reflected backward to its source — that is, to the 
place from which the pulse was originally pro- 
duced by the action of your hand. If, however, 
you hold the string so that its level of tension is 
exactly between perfect rigidity and perfect 
looseness, then the pulse will not be reflected. In 
other words, there will be no reflected wave. 

TRANSMISSION AND REFLEC- 
TION. If two strings are joined end-to-end, 
and a pulse is produced at one end, the pulse 
would, of course, be transmitted to the second 
string. If, however, the second string has a greater 
mass per unit of length than the first one, the 
result would be two pulses: a transmitted pulse 
moving in the “right” direction, and a reflected, 
inverted pulse, moving toward the original 
source of energy. If, on the other hand, the first 
string has a greater mass per unit of length than 
the second one, the reflected pulse would be erect 
(right side up), not inverted. 

For simplicity’s sake, this illustration has 
been presented in terms of a string attached to a 
wall, but, in fact, transmission and reflection 
occur in a number of varieties of wave motion — 


| 2 5 S 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE DF EVERYDAY THINGS 


not just those involving pulses or standing waves. 
A striking example occurs when light hits an 
ordinary window. The majority of the light, of 
course, is transmitted through the window pane, 
but a portion is reflected. Thus, as one looks 
through the window, one also sees one’s re- 
flection. 

Similarly, sound waves are reflected depend- 
ing on the medium with which they are in con- 
tact. A canyon wall, for instance, will reflect a 
great deal of sound, and, thus, it is easy to pro- 
duce an echo in such a situation. On the other 
hand, there are many instances in which the 
desire is to “absorb” sound by transmitting it to 
some other form of material. Thus, for example, 
the lobby of an upscale hotel will include a num- 
ber of plants, as well as tapestries and various 
wall hangings. In addition to adding beauty, 
these provide a medium into which the sound of 
voices and other noises can be transmitted and, 
thus, absorbed. 

Sdund Waves 

production. The experience of 
sound involves production, or the generation of 
sound waves; transmission, or the movement of 
those waves from their source; and reception, the 
principal example of which is hearing. Sound 
itself is discussed in detail elsewhere. Of primary 
concern here is the transmission, and to a lesser 
extent, the production of sound waves. 

In terms of production, sound waves are, as 
noted, longitudinal waves: changes in pressure, 
or alternations between condensation and rar- 
efaction. Vibration is integral to the generation of 
sound. When the diaphragm of a loudspeaker 
pushes outward, it forces nearby air molecules 
closer together, creating a high-pressure region 
all around the loudspeaker. The loudspeaker’s 
diaphragm is pushed backward in response, thus 
freeing up a volume of space for the air mole- 
cules. These, then, rush toward the diaphragm, 
creating a low-pressure region behind the high- 
pressure one. As a result, the loudspeaker sends 
out alternating waves of high pressure (conden- 
sation) and low pressure (rarefaction). 

FREQUENCY AND WAVE- 

LENGTH. As sound waves pass through a 
medium such as air, they create fluctuations 
between condensation and rarefaction. These 
result in pressure changes that cause the listener’s 
eardrum to vibrate with the same frequency as 


the sound wave, a vibration that the ear’s inner 
mechanisms translate and pass on to the brain. 
The range of audibility for the human ear is from 
20 Hz to 20 kHz. The lowest note of the eighty- 
eight keys on a piano is 27 Hz and the highest 
4. 186 kHz. This places the middle and upper reg- 
ister of the piano well within the optimal range 
for audibility, which is between 3 and 4 kHz. 

Sound travels at a speed of about 1,088 ft 
(331 m) per second through air at sea level, and 
the range of sound audible to human ears 
includes wavelengths as large as 11 ft (3.3 m) and 
as small as 1.3 in (3.3 cm). Unlike light waves, 
which are very small, the wavelengths of audible 
sound are comparable to the sizes of ordinary 
objects. This creates an interesting contrast 
between the behaviors of sound and light when 
confronted with an obstacle to their trans- 
mission. 

It is fairly easy to block out light by simply 
holding up a hand in front of one’s eyes. When 
this happens, the Sun casts a shadow on the other 
side of one’s hand. The same action does not 
work with one’s ears and the source of a sound, 
however, because the wavelengths of sound are 
large enough to go right past a relatively small 
object such as a hand. However, if one were to 
put up a tall, wide cement wall between oneself 
and the source of a sound — as is often done in 
areas where an interstate highway passes right by 
a residential community — the object would be 
sufficiently large to block out much of the sound. 

Radio Waves 

Radio waves, like visible light waves, are part of 
the electromagnetic spectrum. They are charac- 
terized by relatively long wavelengths and low 
frequencies — low, that is, in contrast to the much 
higher frequencies of both visible and invisible 
light waves. The frequency range of radio is 
between 10 KHz and about 2,000 MHz — in other 
words, from 10,000 Hz to as much as 2 billion 
Hz — an impressively wide range. 

AM radio broadcasts are found between 0.6 
and 1.6 MHz, and FM broadcasts between 88 and 
108 MHz. Thus, FM is at a much, much higher 
frequency than AM, with the lowest frequency on 
the FM dial 55 times as great as the highest on the 
AM dial. There are other ranges of frequency 
assigned by the FCC (Federal Communications 
Commission) to other varieties of radio trans- 


wave 


SCIENCE DF EVERYDAY THINGS 


VDLUME 2: REAL-LIFE PHYSICS 


MOTION 


259 


Wave Motion 


KEY TERMS 


amplitude: The maximum displace- 

ment of particles in oscillation from their 
normal position. For an ocean wave, 
amplitude is the distance from either the 
crest or the trough to the level that the 
ocean would maintain if it were per- 
fectly still. 

energy: The ability to perform work, 

which is the exertion of force over a given 
distance. Work is the product of force and 
distance, where force and distance are 
exerted in the same direction. 

frequency: The number of waves 

passing through a given point during the 
interval of one second. The higher the fre- 
quency, the shorter the wavelength. Fre- 
quency can also be mathematically related 
to wave speed and period. 

harmonic motion: The repeated 

movement of a particle about a position of 
equilibrium, or balance. 

hertz: A unit for measuring frequen- 

cy, equal to one cycle per second. If a sound 
wave has a frequency of 20,000 Hz, this 


means that 20,000 waves are passing 
through a given point during the interval 
of one second. Higher frequencies are 
expressed in terms of kilohertz (kHz; 10 3 
or 1,000 cycles per second) or megahertz 
(MHz; 10 6 or 1 million cycles per second). 

kinetic energy: The energy that 

an object possesses due to its motion, as 
with a sled when sliding down a hill. This is 
contrasted with potential energy. 

longitudinal wave: A wave in 

which the movement of vibration is in the 
same direction as the wave itself. This is 
contrasted to a transverse wave. 

matter: Physical substance that has 

mass; occupies space; is composed of 
atoms; and is ultimately convertible to 
energy. 

mechanical wave: A type of wave 

that involves matter. Ocean waves are 
mechanical waves; so, too, are the waves 
produced by pulling a string. The matter 
itself may move in place, but, as with all 


| zea 


mission: for instance, citizens’ band (CB) radios 
are in a region between AM and FM, ranging 
from 26.985 MHz to 27.405 MHz. 

Frequency does not indicate power. The 
power of a radio station is a function of the 
wattage available to its transmitter: hence, radio 
stations often promote themselves with 
announcements such as “operating with 100,000 
watts of power....” Thus, an AM station, though it 
has a much lower frequency than an FM station, 
may possess more power, depending on the 
wattage of the transmitter. Indeed, as we shall see, 
it is precisely because of its high frequency that 
an FM station lacks the broadcast range of an 
AM station. 

VDLUME 2: REAL-LIFE PHYSICS 


AMPLITUDE and frequency 

m □ d u l at i □ n s . What is the difference 
between AM and FM? Or to put it another way, 
why is it that an AM station may be heard 
halfway across the country, yet its sound on a car 
radio fades out when the car goes under an over- 
pass? The difference relates to how the various 
radio signals are modulated. 

A radio signal is simply a carrier: it may 
carry Morse code, or it may carry complex 
sounds, but in order to transmit voices and 
music, its signal must be modulated. This can be 
done, for instance, by varying the instantaneous 
amplitude of the radio wave, which is a function 
of the radio station’s power. These variations in 
amplitude are called amplitude modulation, or 

SCIENCE DF EVERYDAY THINGS 



Wave Motion 


KEY TERMS continued 


types of wave motion, there is no net 
movement of matter — only of energy. 

oscillation: A type of harmonic 

motion, typically periodic, in one or more 
dimensions. 

period: For wave motion, a period is 

the amount of time required to complete 
one full cycle of the wave, from trough to 
crest and back to trough. Period can be 
mathematically related to frequency, wave- 
length, and wave speed. 
periodic motion: Motion that is 

repeated at regular intervals. These inter- 
vals are known as periods. 
periodic wave: A wave in which a 

uniform series of crests and troughs follow 
one after the other in regular succession. 
By contrast, the wave produced by apply- 
ing a pulse to a stretched string does not 
follow regular, repeated patterns. 
potential energy: The energy 

that an object possesses due to its position, 
as for instance with a sled at the top of a 
hill. This is contrasted with kinetic energy. 


pulse: An isolated, non-periodic dis- 

turbance that takes place in wave motion of 
a type other than that of a periodic wave. 
standing wave: A type of trans- 

verse wave produced by causing vibrations 
on a string or other piece of material whose 
ends are fixed in place. 

s u r fa c e wav e : A wave that exhibits 

the behavior of both a transverse wave and 
a longitudinal wave. 

transverse wave: A wave in 

which the vibration or motion is perpendi- 
cular to the direction in which the wave is 
moving. This is contrasted to a longitudi- 
nal wave. 

wavelength: The distance between 

a crest and the adjacent crest, or the trough 
and an adjacent trough, of a wave. Wave- 
length, abbreviated X (the Greek letter 
lambda) is mathematically related to wave 
speed, period, and frequency. 

wave motion: Activity that carries 

energy from one place to another without 
actually moving any matter. 


AM, and this was the first type of commercial 
radio to appear. Developed in the period before 
World War I, AM made its debut as a popular 
phenomenon shortly after the war. 

Ironically, FM (frequency modulation) was 
developed not long after AM, but it did not 
become commercially viable until well after 
World War II. As its name suggests, frequency 
modulation involves variation in the signal’s fre- 
quency. The amplitude stays the same, and this — 
combined with the high frequency — produces a 
nice, even sound for FM radio. 

But the high frequency also means that FM 
signals do not travel as far. If a person is listening 
to an FM station while moving away from the 

SCIENCE GF EVERYDAY THINGS 


station’s signal, eventually the station will be 
below the horizon relative to the car, and the car 
radio will no longer be able to receive the signal. 
In contrast to the direct, or line-of-sight, trans- 
missions of FM stations, AM signals (with their 
longer wavelengths) are reflected off of layers in 
Earth’s ionosphere. As a result, a nighttime signal 
from a “clear channel station” may be heard 
across much of the continental United States. 

WHERE TD LEARN M □ R E 

Ardley, Neil. Sound Waves to Music. New York: Glouces- 
ter Press, 1990. 

Berger, Melvin and Gilda Berger. What Makes an Ocean 
Wave?: Questions and Answers About Oceans and 
Ocean Life. New York: Scholastic, 2001. 

VDLUME 2: REAL-LIFE PHYSICS 


26 1 



Wave Motion 


Catherall, Ed. Exploring Sound. Austin, TX: Steck- 
Vaughn Library, 1990. 

Glover, David. Sound and Light. New York: Kingfisher 
Books, 1993. 

“Longitudinal and Transverse Wave Motion” (Web site). 
<http://www.kettering.edu/~drussell/Demos/waves/ 
wavemotion.html> (April 22, 2001). 

“Multimedia Activities: Wave Motion.” ExploreScience.com 
(Web site), <http://www.explorescience.com/ 
activities/activity_list.cfm?catego ryID=3> (April 22, 
2001 ). 


Ruchlis, Hyman. Bathtub Physics. Edited by Donald Barr; 
illustrated by Ray Skibinski. New York: Harcourt, 
Brace, and World, 1967. 

“Wave Motion” (Web site). 

<http://www.media.uwe.ac.uk/masoud/projects/ 
water/wave.html> (April 22, 2001). 

“Wave Motion and Sound.” The Physics Web (Web site). 
<http://www.hcrhs.hunterdon.kl2.nj.us/disk2/ 
Physics/wave.html> (April 22, 2001). 

“Wave Motion Menu.”Carson City-Crystal ELigh School 
Physics and Chemistry Departments (Web site). 
<http://members.aol.com/cepeirce/b2.html> (April 
22, 2001). 


| 262 


VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF 


E V E R Y D AY 


THINGS 


□ S C I L L AT I □ N 


C □ N C E PT 

When a particle experiences repeated movement 
about a position of stable equilibrium, or bal- 
ance, it is said to be in harmonic motion, and if 
this motion is repeated at regular intervals, it is 
called periodic motion. Oscillation is a type of 
harmonic motion, typically periodic, in one or 
more dimensions. Among the examples of oscil- 
lation in the physical world are the motion of a 
spring, a pendulum, or even the steady back-and- 
forth movement of a child on a swing. 

H □ W IT WDRKS 

Stable and Unstable Equilib- 
rium 

When a state of equilibrium exists, the vector 
sum of the forces on an object is equal to zero. 
There are three varieties of equilibrium: stable, 
unstable, and neutral. Neutral equilibrium, dis- 
cussed in the essay on Statics and Equilibrium 
elsewhere in this book, does not play a significant 
role in oscillation; on the other hand, stable and 
unstable equilibrium do. 

In the example of a playground swing, when 
the swing is simply hanging downward — either 
empty or occupied — it is in a position of stable 
equilibrium. The vector sums are balanced, 
because the swing hangs downward with a force 
(its weight) equal to the force of the bars on the 
swing set that hold it up. If it were disturbed 
from this position, as, for instance, by someone 
pushing the swing, it would tend to return to its 
original position. 

If, on the other hand, the swing were raised 
to a certain height — if, say, a child were swinging 

SCIENCE □ F EVERYDAY THINGS 


and an adult caught the child at the point of 
maximum displacement — this would be an 
example of unstable equilibrium. The swing is in 
equilibrium because the forces on it are balanced: 
it is being held upward with a force equal to its 
weight. Yet, this equilibrium is unstable, because 
a disturbance (for instance, if the adult lets go of 
the swing) will cause it to move. Since the swing 
tends to oscillate, it will move back and forth 
across the position of stable equilibrium before 
finally coming to a rest in the stable position. 

Properties of Oscillation 

There are two basic models of oscillation to con- 
sider, and these can be related to the motion of 
two well-known everyday objects: a spring and a 
swing. As noted below, objects not commonly 
considered “springs,” such as rubber bands, dis- 
play spring-like behavior; likewise one could 
substitute “pendulum” for swing. In any case, it is 
easy enough to envision the motion of these two 
varieties of oscillation: a spring generally oscil- 
lates along a straight line, whereas a swing 
describes an arc. 

Either case involves properties common to 
all objects experiencing oscillation. There is 
always a position of stable equilibrium, and there 
is always a cycle of oscillation. In a single cycle, 
the oscillating particle moves from a certain 
point in a certain direction, then reverses direc- 
tion and returns to the original point. The 
amount of time it takes to complete one cycle is 
called a period, and the number of cycles that 
take place during one second is the frequency of 
the oscillation. Frequency is measured in Hertz 
(Hz), with 1 Hz — the term is both singular and 
plural — equal to one cycle per second. 

VDLUME z: real-life physics 



□ SCILLATIDN 



The bounce provided by a trampoline is due to elastic potential energy. (Photograph by Kevin Fleming/Corbis. 
Reproduced by permission.) 


| 264 


It is easiest to think of a cycle as the move- 
ment from a position of stable equilibrium to 
one of maximum displacement, or the furthest 
possible point from stable equilibrium. Because 
stable equilibrium is directly in the middle of a 
cycle, there are two points of maximum displace- 
ment. For a swing or pendulum, maximum dis- 
placement occurs when the object is at its highest 
point on either side of the stable equilibrium 
position. For example, maximum displacement 
in a spring occurs when the spring reaches the 
furthest point of being either stretched or com- 
pressed. 

The amplitude of a cycle is the maximum 
displacement of particles during a single period 
of oscillation, and the greater the amplitude, the 
greater the energy of the oscillation. When an 
object reaches maximum displacement, it revers- 
es direction, and, therefore, it comes to a stop for 
an instant of time. Thus, the speed of movement 
is slowest at that position, and fastest as it passes 
back through the position of stable equilibrium. 
An increase in amplitude brings with it an 
increase in speed, but this does not lead to a 
change in the period: the greater the ampli- 
tude, the further the oscillating object has to 
move, and, therefore, it takes just as long to com- 
plete a cycle. 

VDLUME 2: REAL-LIFE PHYSICS 


Restoring Force 

Imagine a spring hanging vertically from a ceil- 
ing, one end attached to the ceiling for support 
and the other free to hang. It would thus be in a 
position of stable equilibrium: the spring hangs 
downward with a force equal to its weight, and 
the ceiling pulls it upward with an equal and 
opposite force. Suppose, now, that the spring is 
pulled downward. 

A spring is highly elastic, meaning that it can 
experience a temporary stress and still rebound 
to its original position; by contrast, some objects 
(for instance, a piece of clay) respond to defor- 
mation with plastic behavior, permanently 
assuming the shape into which they were 
deformed. The force that directs the spring back 
to a position of stable equilibrium — the force, in 
other words, which must be overcome when the 
spring is pulled downward — is called a restoring 
force. 

The more the spring is stretched, the greater 
the amount of restoring force that must be over- 
come. The same is true if the spring is com- 
pressed: once again, the spring is removed from a 
position of equilibrium, and, once again, the 
restoring force tends to pull it outward to its 
“natural” position. Here, the example is a spring, 

SCIENCE OF EVERYDAY THINGS 


□ 5C I LLATI □ N 


but restoring force can be understood just as eas- 
ily in terms of a swing: once again, it is the force 
that tends to return the swing to a position of sta- 
ble equilibrium. There is, however, one signifi- 
cant difference: the restoring force on a swing is 
gravity, whereas, in the spring, it is related to the 
properties of the spring itself. 

Elastic Potential Energy 

For any solid that has not exceeded the elastic 
limit — the maximum stress it can endure with- 
out experiencing permanent deformation — 
there is a proportional relationship between force 
and the distance it can be stretched. This is 
expressed in the formula F = ks, where s is the 
distance and k is a constant related to the size and 
composition of the material in question. 

The amount of force required to stretch the 
spring is the same as the force that acts to bring it 
back to equilibrium — that is, the restoring force. 
Using the value of force, thus derived, it is possi- 
ble, by a series of steps, to establish a formula for 
elastic potential energy. The latter, sometimes 
called strain potential energy, is the potential 
energy that a spring or a spring-like object pos- 
sesses by virtue of its deformation from the state 
of equilibrium. It is equal to Yiks 2 . 

POTENTIAL AND KINETIC EN- 
ERGY. Potential energy, as its name suggests, 
involves the potential of something to move 
across a given interval of space — for example, 
when a sled is perched at the top of a hill. As it 
begins moving through that interval, the object 
will gain kinetic energy. Hence, the elastic poten- 
tial energy of the spring, when the spring is held 
at a position of the greatest possible displace- 
ment from equilibrium, is at a maximum. Once 
it is released, and the restoring force begins to 
move it toward the equilibrium position, poten- 
tial energy drops and kinetic energy increases. 
But the spring will not just return to equilibrium 
and stop: its kinetic energy will cause it to keep 
going. 

In the case of the “swing” model of oscilla- 
tion, elastic potential energy is not a factor. 
(Unless, of course, the swing itself were suspend- 
ed on some sort of spring, in which case the 
object will oscillate in two directions at once.) 
Nonetheless, all systems of motion involve 
potential and kinetic energy. When the swing is 
at a position of maximum displacement, its 

SCIENCE DF EVERYDAY THINGS 



A BUNGEE JUMPER HELPS ILLUSTRATE A REAL-WORLD 

example of oscillation. (Eye Ubiquitous/Corbis. Reproduced 
by permission.) 

potential energy is at a maximum as well. Then, 
as it moves toward the position of stable equilib- 
rium, it loses potential energy and gains kinetic 
energy. Upon passing through the stable equilib- 

VDLUME 2: REAL-LIFE PHYSICS 


265 


□ SCI LLATI □ N 


| 266 


rium position, kinetic energy again decreases, 
while potential energy increases. The sum of the 
two forms of energy is always the same, but the 
greater the amplitude, the greater the value of 
this sum. 


REAL-LIFE 
A P P L I C AT I □ N S 

Springs and Damping 

Elastic potential energy relates primarily to 
springs, but springs are a major part of everyday 
life. They can be found in everything from the 
shock-absorber assembly of a motor vehicle to 
the supports of a trampoline fabric, and in both 
cases, springs blunt the force of impact. 

If one were to jump on a piece of trampoline 
fabric stretched across an ordinary table — one 
with no springs — the experience would not be 
much fun, because there would be little bounce. 
On the other hand, the elastic potential energy of 
the trampoline’s springs ensures that anyone of 
normal weight who jumps on the trampoline is 
liable to bounce some distance into the air. As a 
person’s body comes down onto the trampoline 
fabric, this stretches the fabric (itself highly elas- 
tic) and, hence, the springs. Pulled from a posi- 
tion of equilibrium, the springs acquire elastic 
potential energy, and this energy makes possible 
the upward bounce. 

As a car goes over a bump, the spring in its 
shock-absorber assembly is compressed, but the 
elastic potential energy of the spring immediate- 
ly forces it back to a position of equilibrium, thus 
ensuring that the bump is not felt throughout the 
entire vehicle. However, springs alone would 
make for a bouncy ride; hence, a modern vehicle 
also has shock absorbers. The shock absorber, a 
cylinder in which a piston pushes down on a 
quantity of oil, acts as a damper — that is, an 
inhibitor of the springs’ oscillation. 

SIMPLE HARMDNIC M □ T I □ N 

and damping. Simple harmonic motion 
occurs when a particle or object moves back and 
forth within a stable equilibrium position under 
the influence of a restoring force proportional to 
its displacement. In an ideal situation, where fric- 
tion played no part, an object would continue to 
oscillate indefinitely. 

VDLUME 2: REAL-LIFE PHYSICS 


Of course, objects in the real world do not 
experience perpetual oscillation; instead, most 
oscillating particles are subject to damping, or 
the dissipation of energy, primarily as a result of 
friction. In the earlier illustration of the spring 
suspended from a ceiling, if the string is pulled to 
a position of maximum displacement and then 
released, it will, of course, behave dramatically at 
first. Over time, however, its movements will 
become slower and slower, because of the damp- 
ing effect of frictional forces. 

hdw damping wdrks. When 
the spring is first released, most likely it will fly 
upward with so much kinetic energy that it will, 
quite literally, bounce off the ceiling. But with 
each transit within the position of equilibrium, 
the friction produced by contact between the 
metal spring and the air, and by contact between 
molecules within the spring itself, will gradually 
reduce the energy that gives it movement. In 
time, it will come to a stop. 

If the damping effect is small, the amplitude 
will gradually decrease, as the object continues to 
oscillate, until eventually oscillation ceases. On 
the other hand, the object may be “overdamped,” 
such that it completes only a few cycles before 
ceasing to oscillate altogether. In the spring illus- 
tration, overdamping would occur if one were to 
grab the spring on a downward cycle, then slow- 
ly let it go, such that it no longer bounced. 

There is a type of damping less forceful than 
overdamping, but not so gradual as the slow dis- 
sipation of energy due to frictional forces alone. 
This is called critical damping. In a critically 
damped oscillator, the oscillating material is 
made to return to equilibrium as quickly as pos- 
sible without oscillating. An example of a criti- 
cally damped oscillator is the shock-absorber 
assembly described earlier. 

Even without its shock absorbers, the 
springs in a car would be subject to some degree 
of damping that would eventually bring a halt to 
their oscillation; but because this damping is of a 
very gradual nature, their tendency is to contin- 
ue oscillating more or less evenly. Over time, of 
course, the friction in the springs would wear 
down their energy and bring an end to their 
oscillation, but by then, the car would most like- 
ly have hit another bump. Therefore, it makes 
sense to apply critical damping to the oscillation 
of the springs by using shock absorbers. 

SCIENCE DF EVERYDAY THINGS 


□ 5C I LLATI □ N 


Bungee Cgrds and Rubber 
Bands 

Many objects in daily life oscillate in a spring-like 
way, yet people do not commonly associate them 
with springs. For example, a rubber band, which 
behaves very much like a spring, possesses high 
elastic potential energy. It will oscillate when 
stretched from a position of stable equilibrium. 

Rubber is composed of long, thin molecules 
called polymers, which are arranged side by side. 
The chemical bonds between the atoms in a 
polymer are flexible and tend to rotate, produc- 
ing kinks and loops along the length of the mol- 
ecule. The super-elastic polymers in rubber are 
called elastomers, and when a piece of rubber is 
pulled, the kinks and loops in the elastomers 
straighten. 

The structure of rubber gives it a high degree 
of elastic potential energy, and in order to stretch 
rubber to maximum displacement, there is a 
powerful restoring force that must be overcome. 
This can be illustrated if a rubber band is 
attached to a ceiling, like the spring in the earlier 
example, and allowed to hang downward. If it is 
pulled down and released, it will behave much as 
the spring did. 

The oscillation of a rubber band will be even 
more appreciable if a weight is attached to the 
“free” end — that is, the end hanging downward. 
This is equivalent, on a small scale, to a bungee 
jumper attached to a cord. The type of cord used 
for bungee jumping is highly elastic; otherwise, 
the sport would be even more dangerous than it 
already is. Because of the cord’s elasticity, when 
the bungee jumper “reaches the end of his rope,” 
he bounces back up. At a certain point, he begins 
to fall again, then bounces back up, and so on, 
oscillating until he reaches the point of stable 
equilibrium. 

The Pendulum 

As noted earlier, a pendulum operates in much 
the same way as a swing; the difference between 
them is primarily one of purpose. A swing exists 
to give pleasure to a child, or a certain bittersweet 
pleasure to an adult reliving a childhood experi- 
ence. A pendulum, on the other hand, is not for 
play; it performs the function of providing a 
reading, or measurement. 

SCIENCE □ E EVERYDAY THINGS 


One type of pendulum is a metronome, 
which registers the tempo or speed of music. 
Housed in a hollow box shaped like a pyramid, a 
metronome consists of a pendulum attached to a 
sliding weight, with a fixed weight attached to the 
bottom end of the pendulum. It includes a num- 
ber scale indicating the number of oscillations 
per minute, and by moving the upper weight, 
one can change the beat to be indicated. 

ZHANG HENG’S SEISMQ- 

s c □ p e . Metronomes were developed in the 
early nineteenth century, but, by then, the con- 
cept of a pendulum was already old. In the sec- 
ond century a.d., Chinese mathematician and 
astronomer Zhang Heng (78-139) used a pendu- 
lum to develop the world’s first seismoscope, an 
instrument for measuring motion on Earth’s sur- 
face as a result of earthquakes. 

Zhang Heng’s seismoscope, which he 
unveiled in 132 a.d., consisted of a cylinder sur- 
rounded by bronze dragons with frogs (also 
made of bronze) beneath. When the earth shook, 
a ball would drop from a dragon’s mouth into 
that of a frog, making a noise. The number of 
balls released, and the direction in which they 
fell, indicated the magnitude and location of the 
seismic disruption. 

CLDCKS, SCIENTIFIC INSTRU- 
MENTS, AND “FAX MACHINE”. In 

718 a.d., during a period of intellectual flowering 
that attended the early T’ang Dynasty (618-907), 
a Buddhist monk named I-hsing and a military 
engineer named Liang Ling-tsan built an astro- 
nomical clock using a pendulum. Many clocks 
today — for example, the stately and imposing 
“grandfather clock” found in some homes — like- 
wise, use a pendulum to mark time. 

Physicists of the early modern era used pen- 
dula (the plural of pendulum) for a number of 
interesting purposes, including calculations 
regarding gravitational force. Experiments with 
pendula by Galileo Galilei (1564-1642) led to the 
creation of the mechanical pendulum clock — the 
grandfather clock, that is — by distinguished 
Dutch physicist and astronomer Christiaan Huy- 
gens (1629-1695). 

In the nineteenth century, A Scottish inven- 
tor named Alexander Bain (1810-1877) even 
used a pendulum to create the first “fax 
machine.” Using matching pendulum transmit- 
ters and receivers that sent and received electrical 

VGLUME z: REAL-LIFE PHYSICS 


267 


□ SCI LLATI □ N 


KEY TERMS 


amplitude: The maximum displace- 

ment of particles from their normal posi- 
tion during a single period of oscillation. 

cycle: One full repetition of oscilla- 

tion. In a single cycle, the oscillating parti- 
cle moves from a certain point in a certain 
direction, then switches direction and 
moves back to the original point. Typically, 
this is from the position of stable equilibri- 
um to maximum displacement and back 
again to the stable equilibrium position. 
damping: The dissipation of energy 

during oscillation, which prevents an 
object from continuing in simple harmon- 
ic motion and will eventually force it to 
stop oscillating altogether. Damping is 
usually caused by friction. 

ELASTIC POTENTIAL ENERGY: 

The potential energy that a spring or a 
spring-like object possesses by virtue of its 
deformation from the state of equilibrium. 
Sometimes called strain potential energy, it 
is equal to l AKS 2 , WHERE S is the distance 
stretched and k is a figure related to the 
size and composition of the material in 
question. 

equilibrium: A state in which the 

vector sum for all lines of force on an 
object is equal to zero. 


frequency: For a particle experi- 

encing oscillation, frequency is the number 
of cycles that take place during one second. 
Frequency is measured in Hertz. 

friction: The force that resists 

motion when the surface of one object 
comes into contact with the surface of 
another. 

harmonic motidn: The repeated 

movement of a particle within a position of 
equilibrium, or balance. 

hertz: A unit for measuring frequen- 

cy. The number of Hertz is the number of 
cycles per second. 

kinetic energy: The energy that 

an object possesses due to its motion, as 
with a sled, when sliding down a hill. This 
is contrasted with potential energy. 

MAXIMUM DISPLACEMENT: Foran 

object in oscillation, maximum displace- 
ment is the furthest point from stable equi- 
librium. Since stable equilibrium is in the 
middle of a cycle, there are two points of 
maximum displacement. For a swing or 
pendulum, this occurs when the object is at 
its highest point on either side of the stable 
equilibrium position. Maximum displace- 


| 268 


impulses, he created a crude device that, at the 
time, seemed to have little practical purpose. In 
fact, Bain’s “fax machine,” invented in 1840, was 
more than a century ahead of its time. 

THE FOUCAULT PENDULUM. 

By far the most important experiments with pen- 
dula during the nineteenth century, however, 
were those of the French physicist Jean Bernard 
Leon Foucault (1819-1868). Swinging a heavy 
iron ball from a wire more than 200 ft (61 m) in 

VOLUME 2: REAL-LIFE PHYSICS 


length, he was able to demonstrate that Earth 
rotates on its axis. 

Foucault conducted his famous demonstra- 
tion in the Pantheon, a large domed building in 
Paris named after the ancient Pantheon of Rome. 
He arranged to have sand placed on the floor of 
the Pantheon, and placed a pin on the bottom of 
the iron ball, so that it would mark the sand as 
the pendulum moved. A pendulum in oscillation 
maintains its orientation, yet the Foucault pen- 

SCIENCE GF EVERYDAY THINGS 



□ 5C I LLATI □ N 


KEY TERMS continued 


ment in a spring occurs when the spring is 
either stretched or compressed as far as it 
will go. 

qsc illation: A type of harmonic 

motion, typically periodic, in one or more 
dimensions. 

periqd: The amount of time required 

for one cycle in oscillating motion — for 
instance, from a position of maximum dis- 
placement to one of stable equilib- 
rium, and, once again, to maximum dis- 
placement. 

periodic motion: Motion that is 

repeated at regular intervals. These inter- 
vals are known as periods. 

potential energy: The energy 

that an object possesses due to its position, 
as for instance, with a sled at the top of a 
hill. This is contrasted with kinetic energy. 

restoring force: A force that 

directs an object back to a position of sta- 
ble equilibrium. An example is the resist- 
ance of a spring, when it is extended. 

SIMPLE HARMONIC MOTION: Har- 

monic motion, in which a particle moves 
back and forth about a stable equilibrium 


position under the influence of a restoring 
force proportional to its displacement. 
Simple harmonic motion is, in fact, an 
ideal situation; most types of oscillation 
are subject to some form of damping. 

STABLE EQUILIBRIUM: A type of 

equilibrium in which, if an object were dis- 
turbed, it would tend to return to its origi- 
nal position. For an object in oscillation, 
stable equilibrium is in the middle of a 
cycle, between two points of maximum 
displacement. 

vector: A quantity that possesses 

both magnitude and direction. 

vector sum: A calculation that 

yields the net result of all the vectors 
applied in a particular situation. Because 
direction is involved, it is necessary when 
calculating the vector sum of forces on an 
object (as, for instance, when determining 
whether or not it is in a state of equilibri- 
um), to assign a positive value to forces in 
one direction, and a negative value to 
forces in the opposite direction. If the 
object is in equilibrium, these forces will 
cancel one another out. 


dulum (as it came to be called) seemed to be 
shifting continually toward the right, as indicated 
by the marks in the sand. 

The confusion related to reference point: 
since Earth’s rotation is not something that can 
be perceived with the senses, it was natural to 
assume that the pendulum itself was changing 
orientation — or rather, that only the pendulum 
was moving. In fact, the path of Foucault’s pen- 
dulum did not vary nearly as much as it seemed. 

SCIENCE GF EVERYDAY THINGS 


Earth itself was moving beneath the pendulum, 
providing an additional force which caused the 
pendulum’s plane of oscillation to rotate. 

WHERE TD LEARN MORE 

Brynie, Faith Hickman. Six-Minute Science Experiments. 
Illustrated by Kim Whittingham. New York: Sterling 
Publishing Company, 1996. 

Ehrlich, Robert. Turning the World Inside Out, and 174 
Other Simple Physics Demonstrations. Princeton, N.J.: 
Princeton University Press, 1990. 


VDLUME 2: REAL-LIFE PHYSICS 


269 



□ SCI LLATI □ N 


“Foucault Pendulum” Smithsonian Institution FAQs (Web 
site), <http://www.si.edu/resource/faq/nmah/pendu- 
lum.html> (April 23, 2001). 

Kruszelnicki, Karl S. The Foucault Pendulum (Web site). 
<http://www.abc.net.au/surf/pendulum/pendulum. 
html> (April 23, 2001). 

Schaefer, Lola M. Back and Forth. Edited by Gail Saun- 
ders-Smith; P. W. Hammer, consultant. Mankato, 
MN: Pebble Books, 2000. 


Shirley, Jean. Galileo. Illustrated by Raymond Renard. St. 
Louis: McGraw-Hill, 1967. 

Suplee, Curt. Everyday Science Explained. Washington, 
D.C.: National Geographic Society, 1996. 

Topp, Patricia. This Strange Quantum World and You. 

Nevada City, CA: Blue Dolphin, 1999. 

Zubrowski, Bernie. Making Waves: Finding Out About 
Rhythmic Motion. Illustrated by Roy Doty. New York: 
Morrow Junior Books, 1994. 


| 27D 


VOLUME 2: REAL-LIFE PHYSICS 


SCIENCE 


OF EVERYD AY 


THINGS 


FREQUENCY 


C □ N C E PT 

Everywhere in daily life, there are frequencies of 
sound and electromagnetic waves, constantly 
changing and creating the features of the visible 
and audible world familiar to everyone. Some 
aspects of frequency can only be perceived indi- 
rectly, yet people are conscious of them without 
even thinking about it: a favorite radio station, 
for instance, may have a frequency of 99.7 MHz, 
and fans of that station knows that every time 
they turn the FM dial to that position, the sta- 
tion’s signal will be there. Of course, people can- 
not “hear” radio and television frequencies — 
part of the electromagnetic spectrum — but the 
evidence for them is everywhere. Similarly, peo- 
ple are not conscious, in any direct sense, of fre- 
quencies in sound and light — yet without differ- 
ences in frequency, there could be no speech or 
music, nor would there be any variations of 
color. 

H □ W IT WDRKS 

Harmonic Motion and Energy 

In order to understand frequency, it is first neces- 
sary to comprehend two related varieties of 
movement: oscillation and wave motion. Both 
are examples of a broader category, periodic 
motion: movement that is repeated at regular 
intervals called periods. Oscillation and wave 
motion are also examples of harmonic motion, 
or the repeated movement of a particle about a 
position of equilibrium, or balance. 

KINETIC AND POTENTIAL EN- 
ERGY. In harmonic motion, and in some 
types of periodic motion, there is a continual 

SCIENCE DF EVERYDAY THINGS 


conversion of energy from one form to another. 
On the one hand is potential energy, or the ener- 
gy of an object due to its position and, hence, its 
potential for movement. On the other hand, 
there is kinetic energy, the energy of movement 
itself. 

Potential-kinetic conversions take place con- 
stantly in daily life: any time an object is at a dis- 
tance from a position of stable equilibrium, and 
some force (for instance, gravity) is capable of 
moving it to that position, it possesses potential 
energy. Once it begins to move toward that equi- 
librium position, it loses potential energy and 
gains kinetic energy. Likewise, a wave at its crest 
has potential energy, and gains kinetic energy as 
it moves toward its trough. Similarly, an oscillat- 
ing object that is as far as possible from the sta- 
ble-equilibrium position has enormous potential 
energy, which dissipates as it begins to move 
toward stable equilibrium. 

v i b r at i □ n . Though many examples 
of periodic and harmonic motion can be found 
in daily life, the terms themselves are certainly 
not part of everyday experience. On the other 
hand, everyone knows what “vibration” means: 
to move back and forth in place. Oscillation, dis- 
cussed in more detail below, is simply a more sci- 
entific term for vibration; and while waves are 
not themselves merely vibrations, they involve — 
and may produce — vibrations. This, in fact, is 
how the human ear hears: by interpreting vibra- 
tions resulting from sound waves. 

Indeed, the entire world is in a state of vibra- 
tion, though people seldom perceive this move- 
ment — except, perhaps, in dramatic situations 
such as earthquakes, when the vibrations of 
plates beneath Earth’s surface become too force- 

VDLUME Z: REAL-LIFE PHYSICS 


27 t 



Frequency 


| 272 



Grandfather clocks are one of the best-known 
va rieties of a pendulum. (Photograph by Peter 
Harholdt/Corbis. Reproduced by permission.) 


ful to ignore. All matter vibrates at the molecular 
level, and every object possesses what is called a 
natural frequency, which depends on its size, 
shape, and composition. This explains how a 
singer can shatter a glass by hitting a certain note, 
which does not happen because the singer’s voice 
has reached a particularly high pitch; rather, it is 
a matter of attaining the natural frequency of the 
glass. As a result, all the energy in the sound of 
the singer’s voice is transferred to the glass, and it 
shatters. 

Oscillation 

Oscillation is a type of harmonic motion, typi- 
cally periodic, in one or more dimensions. There 
are two basic types of oscillation: that of a swing 
or pendulum and that of a spring. In each case, 
an object is disturbed from a position of stable 
equilibrium, and, as a result, it continues to move 
back and forth around that stable equilibrium 
position. If a spring is pulled from stable equilib- 
rium, it will generally oscillate along a straight 
path; a swing, on the other hand, will oscillate 
along an arc. 


In oscillation, whether the oscillator be 
spring-like or swing-like, there is always a cycle in 
which the oscillating particle moves from a cer- 
tain point in a certain direction, then reverses 
direction and returns to the original point. Usu- 
ally a cycle is viewed as the movement from a 
position of stable equilibrium to one of maxi- 
mum displacement, or the furthest possible 
point from stable equilibrium. Because stable 
equilibrium is directly in the middle of a cycle, 
there are two points of maximum displacement: 
on a swing, this occurs when the object is at its 
highest point on either side of the stable equilib- 
rium position, and on a spring, maximum dis- 
placement occurs when the spring is either 
stretched or compressed as far as it will go. 

Wave Motion 

Wave motion is a type of harmonic motion that 
carries energy from one place to another without 
actually moving any matter. While oscillation 
involves the movement of “an object,” whether it 
be a pendulum, a stretched rubber band, or some 
other type of matter, a wave may or may not 
involve matter. Example of a wave made out of 
matter — that is, a mechanical wave — is a wave on 
the ocean, or a sound wave, in which energy 
vibrates through a medium such as air. Even in 
the case of the mechanical wave, however, the 
matter does not experience any net displacement 
from its original position. (Water molecules do 
rotate as a result of wave motion, but they end up 
where they began.) 

There are waves that do not follow regular, 
repeated patterns; however, within the context of 
frequency, our principal concern is with periodic 
waves, or waves that follow one another in regu- 
lar succession. Examples of periodic waves 
include ocean waves, sound waves, and electro- 
magnetic waves. 

Periodic waves may be further divided into 
transverse and longitudinal waves. A transverse 
wave is the shape that most people imagine when 
they think of waves: a regular up-and-down pat- 
tern (called “sinusoidal” in mathematical terms) 
in which the vibration or motion is perpendicu- 
lar to the direction the wave is moving. 

A longitudinal wave is one in which the 
movement of vibration is in the same direction 
as the wave itself. Though these are a little hard- 
er to picture, longitudinal waves can be visual- 
ized as a series of concentric circles emanating 


VDLUME 2: REAL-LIFE PHYSICS 


SCIENCE OF EVERYDAY THINGS 



from a single point. Sound waves are longitudi- 
nal: thus when someone speaks, waves of sound 
vibrations radiate out in all directions. 

Amplitu de 

There are certain properties of waves, such as 
wavelength, or the distance between waves, that 
are not properties of oscillation. However, both 
types of motion can be described in terms of 
amplitude, period, and frequency. The first of 
these is not related to frequency in any mathe- 
matical sense; nonetheless, where sound waves 
are concerned, both amplitude and frequency 
play a significant role in what people hear. 

Though waves and oscillators share the 
properties of amplitude, period, and frequency, 
the definitions of these differ slightly depending 
on whether one is discussing wave motion or 
oscillation. Amplitude, generally speaking, is the 
value of maximum displacement from an aver- 
age value or position — or, in simpler terms, 
amplitude is “size.” For an object experiencing 
oscillation, it is the value of the object’s maxi- 
mum displacement from a position of stable 
equilibrium during a single period. It is thus the 
“size” of the oscillation. 

In the case of wave motion, amplitude is also 
the “size” of a wave, but the precise definition 
varies, depending on whether the wave in ques- 
tion is transverse or longitudinal. In the first 
instance, amplitude is the distance from either 
the crest or the trough to the average position 
between them. For a sound wave, which is longi- 
tudinal, amplitude is the maximum value of the 
pressure change between waves. 

Peridd and Frequency 

Unlike amplitude, period is directly related to 
frequency. For a transverse wave, a period is the 
amount of time required to complete one full 
cycle of the wave, from trough to crest and back 
to trough. In a longitudinal wave, a period is the 
interval between waves. With an oscillator, a peri- 
od is the amount of time it takes to complete one 
cycle. The value of a period is usually expressed 
in seconds. 

Frequency in oscillation is the number of 
cycles per second, and in wave motion, it is the 
number of waves that pass through a given point 
per second. These cycles per second are called 
Hertz (Hz) in honor of nineteenth-century Ger- 

SCIENCE □ E EVERYDAY THINGS 



Middle C — which is at the middle of a piano key- 
board IS THE STARTING POINT OF A BASIC MUSICAL 

SCALE. It is called the fundamental frequency, 
or the first harmonic. (Photograph by Francoise 
Gervais/Corbis. Reproduced by permission.) 

man physicist Heinrich Rudolf Hertz (1857- 
1894), who greatly advanced understanding of 
electromagnetic wave behavior during his short 
career. 

If something has a frequency of 100 Hz, this 
means that 100 waves are passing through a given 
point during the interval of one second, or that 
an oscillator is completing 100 cycles in a second. 
Higher frequencies are expressed in terms of 
kilohertz (kHz; 10 3 or 1,000 cycles per second); 
megahertz (MHz; 10 6 or 1 million cycles per sec- 
ond); and gigahertz (GHz; 10 9 or 1 billion cycles 
per second.). 

A clear mathematical relationship exists 
between period, symbolized by T, and frequency 
(/): each is the inverse of the other. Hence, 

T = J- 

/, 

and 


VDLUME 2: REAL-LIFE PHYSICS 


FREQUENCY 


273 



Frequency 


| 274 


If an object in harmonic motion has a fre- 
quency of 50 Hz, its period is 1/50 of a second 
(0.02 sec). Or, if it has a period of 1/20,000 of a 
second (0.00005 sec), that means it has a fre- 
quency of 20,000 Hz. 

REAL-LIFE 
A P P L I C AT I □ N S 

Grandfather Clocks and 
M ETRONOMES 

One of the best-known varieties of pendulum 
(plural, pendula) is a grandfather clock. Its 
invention was an indirect result of experiments 
with pendula by Galileo Galilei (1564-1642), 
work that influenced Dutch physicist and 
astronomer Christiaan Huygens (1629-1695) in 
the creation of the mechanical pendulum 
clock — or grandfather clock, as it is commonly 
known. 

The frequency of a pendulum, a swing-like 
oscillator, is the number of “swings” per minute. 
Its frequency is proportional to the square root of 
the downward acceleration due to gravity (32 ft 
or 9.8 m/sec 2 ) divided by the length of the pen- 
dulum. This means that by adjusting the length 
of the pendulum on the clock, one can change its 
frequency: if the pendulum length is shortened, 
the clock will run faster, and if it is lengthened, 
the clock will run more slowly. 

Another variety of pendulum, this one dat- 
ing to the early nineteenth century, is a 
metronome, an instrument that registers the 
tempo or speed of music. Consisting of a pendu- 
lum attached to a sliding weight, with a fixed 
weight attached to the bottom end of the pendu- 
lum, a metronome includes a number scale indi- 
cating the frequency — that is, the number of 
oscillations per minute. By moving the upper 
weight, one can speed up or slow down the beat. 

Harmqnics 

As noted earlier, the volume of any sound is 
related to the amplitude of the sound waves. Fre- 
quency, on the other hand, determines the pitch 
or tone. Though there is no direct correlation 
between intensity and frequency, in order for a 
person to hear a very low-frequency sound, it 
must be above a certain decibel level. 

The range of audibility for the human ear is 
from 20 Hz to 20,000 Hz. The optimal range for 
hearing, however, is between 3,000 and 4,000 Hz. 

VDLUME 2: REAL-LIFE PHYSICS 


This places the piano, whose 88 keys range from 
27 Hz to 4,186 Hz, well within the range of 
human audibility. Many animals have a much 
wider range: bats, whales, and dolphins can hear 
sounds at a frequency up to 150,000 Hz. But 
humans have something that few animals can 
appreciate: music, a realm in which frequency 
changes are essential. 

Each note has its own frequency: middle C, 
for instance, is 264 Hz. But in order to produce 
what people understand as music — that is, pleas- 
ing combinations of notes — it is necessary to 
employ principles of harmonics, which express 
the relationships between notes. These mathe- 
matical relations between musical notes are 
among the most intriguing aspects of the con- 
nection between art and science. 

It is no wonder, perhaps, that the great Greek 
mathematician Pythagoras (c. 580-500 b.c.) 
believed that there was something spiritual or 
mystical in the connection between mathematics 
and music. Pythagoras had no concept of fre- 
quency, of course, but he did recognize that there 
were certain numerical relationships between the 
lengths of strings, and that the production of 
harmonious music depended on these ratios. 

RATIOS DF FREQUENCY AND 

pleasing tones. Middle C — located,, 
appropriately enough, in the middle of a piano 
keyboard — is the starting point of a basic musi- 
cal scale. It is called the fundamental frequency, 
or the first harmonic. The second harmonic, one 
octave above middle C, has a frequency of 528 
Hz, exactly twice that of the first harmonic; and 
the third harmonic (two octaves above middle C) 
has a frequency of 792 cycles, or three times that 
of middle C. So it goes, up the scale. 

As it turns out, the groups of notes that peo- 
ple consider harmonious just happen to involve 
specific whole-number ratios. In one of those 
curious interrelations of music and math that 
would have delighted Pythagoras, the smaller the 
numbers involved in the ratios, the more pleasing 
the tone to the human psyche. 

An example of a pleasing interval within an 
octave is a fifth, so named because it spans five 
notes that are a whole step apart. The C Major 
scale is easiest to comprehend in this regard, 
because it does not require reference to the “black 
keys,” which are a half-step above or below the 
“white keys.” Thus, the major fifth in the C- 
Major scale is C, D, E, F, G. It so happens that the 

SCIENCE DF EVERYDAY THINGS 


Frequency 


KEY TERMS 


amplitude: For an object oscillation, 

amplitude is the value of the object’s max- 
imum displacement from a position of sta- 
ble equilibrium during a single period. In a 
transverse wave, amplitude is the distance 
from either the crest or the trough to the 
average position between them. For a 
sound wave, the best-known example of a 
longitudinal wave, amplitude is the maxi- 
mum value of the pressure change between 
waves. 

cycle: In oscillation, a cycle occurs 

when the oscillating particle moves from a 
certain point in a certain direction, then 
switches direction and moves back to the 
original point. Typically, this is from the 
position of stable equilibrium to maxi- 
mum displacement and back again to the 
stable equilibrium position. 

frequency: For a particle experi- 

encing oscillation, frequency is the number 
of cycles that take place during one second. 
In wave motion, frequency is the number 
of waves passing through a given point 
during the interval of one second. In either 
case, frequency is measured in Hertz. 
Period (T) is the mathematical inverse of 
frequency (/) hence f=HT. 

harmonic motion: The repeated 

movement of a particle about a position of 
equilibrium, or balance. 

hertz: A unit for measuring fre- 

quency, named after nineteenth-century 
German physicist Heinrich Rudolf Hertz 


(1857-1894). Higher frequencies are 
expressed in terms of kilohertz (kHz; 10 3 
or 1,000 cycles per second); megahertz 
(MHz; 10 6 or 1 million cycles per second); 
and gigahertz (GHz; 10 9 or 1 billion cycles 
per